Question
![e squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAARCAYAAADQWvz5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAKVJREFUeNpjYCAN/IfiX0B8FIhVGCgETECcBcTnGKgEflDDEHsgPkipIZLQMFKixBA1IN4CNYwil2wDYj5CCsWBeA00EB9CwwEZgAzRIGQIyJZLQOwH5WsB8RUc6QgZY4AuIK5EEwOFBRupCewDEIuiiX2C0kQDcxzOPkpqbIDCZRU1UqklEJ+kVr65BsQF0DARhAa8LTkGgZL7YSD+AzU0mWEgAAAoyiWYZ6Ex8AAAAGB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bWk+ZTwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21hdGg+JeSUYAAAAABJRU5ErkJggg==)
![e cubed](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAARCAYAAADQWvz5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAKpJREFUeNpjYCAN/IfiX0B8AYjdGKgANID4ITUMYgLid5QaIgzEU4A4kRJDYOEUSw1v8QFxKxCnMVAJ/MAlIQ7Ea6AKQDFij8cQWyA+g8u5l4DYD8rXAuIrOMIHZNEOIJbHZlAXEFeiiW0BYjZS08QHIBZFE/sEpYkG5kjORsZHSQ19ULisokY0WgLxSWqliWtAXAANE0FowNuSY5ASEB8G4j9QQ5MZBgIAANwxJg0DeBbEAAAAYHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3VwPjxtaT5lPC9taT48bW4+MzwvbW4+PC9tc3VwPjwvbWF0aD5Ag68mAAAAAElFTkSuQmCC)
![e to the power of 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAARCAYAAADQWvz5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAIhJREFUeNpjYCAdqAFxLRBfYKAQLAbiNCD+z0AlMGoQhQaJA/EaIP4BxA+B2J4cg/iA+BIQ+0H5WkB8BYcB6BgFdAFxJZrYFiBmI8W/TED8AYhF0cQ+QWmigTkOJx8lNQZA4bKKGlFpCcQnqZUurgFxATRMBKEBb0uOQUpAfBiI/0ANTWYYCAAANuEkTINhQJgAAABgdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1pPmU8L21pPjxtbj4xPC9tbj48L21zdXA+PC9tYXRoPopN2aoAAAAASUVORK5CYII=)
- e
Hint:
The initial form for the limit is indeterminate
to the power of infinity So, use the formula. In this question, we have to find value of
.
The correct answer is: ![e cubed](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAARCAYAAADQWvz5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAKpJREFUeNpjYCAN/IfiX0B8AYjdGKgANID4ITUMYgLid5QaIgzEU4A4kRJDYOEUSw1v8QFxKxCnMVAJ/MAlIQ7Ea6AKQDFij8cQWyA+g8u5l4DYD8rXAuIrOMIHZNEOIJbHZlAXEFeiiW0BYjZS08QHIBZFE/sEpYkG5kjORsZHSQ19ULisokY0WgLxSWqliWtAXAANE0FowNuSY5ASEB8G4j9QQ5MZBgIAANwxJg0DeBbEAAAAYHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3VwPjxtaT5lPC9taT48bW4+MzwvbW4+PC9tc3VwPjwvbWF0aD5Ag68mAAAAAElFTkSuQmCC)
![text Lt end text subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 5 over denominator x plus 2 end fraction close parentheses to the power of x plus 2 end exponent](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator 1 plus begin display style 5 over x end style over denominator 1 plus begin display style 2 over x end style end fraction close parentheses to the power of x plus 2 end exponent space space space space left parenthesis W e space c a n space w r i t e space space left parenthesis x plus a right parenthesis space equals space x left parenthesis 1 plus a over x right parenthesis. space space space right parenthesis](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator 1 plus begin display style 5 over x end style over denominator 1 plus begin display style 2 over x end style end fraction close parentheses to the power of x plus 2 end exponent equals space space open parentheses fraction numerator 1 plus begin display style a over infinity end style over denominator 1 plus begin display style b over infinity end style end fraction close parentheses to the power of infinity space equals 1 to the power of infinity](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATkAAABYCAYAAACOPoC6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAyCPPDHgAACdRJREFUeNrtnX9kVnscx79mkkxkJklGMsk1kWTmSuRKkolJrmQi2R8zietKJjP6qz9mxpXkuiaSXMlEkkl/XJIkSUx/TSaSZDLjud+P83ncc0/nefY8O+fZvj9ebz62c57teb6fH8/78/1+zjnfjzFxYdjKVMD6TaqO64mKyrKV51b2GADAhuBnK6+stAeso+j22srhkkmsEbQpwb4k1ABYf2yx8sHK/gh0/Ul17ajx+jMrvSliemSluwSSq+I74QbA+mPcynRE+k6qznk4YeWO/n7DyqmSZnJGZ5BzDugfelmiEf8P87WPB11WvljZ6fg4K3WkWeyw8lV1z4Ms20et3CxxLPKZUpPbTVnCm7LFJU1405lVzoCVW0qWe6EQ93HFyl8ejLNS8vtJkF6tk+nfWdlU0rh6rDxUoqMs4UfZQr4Xg+q7SfXzsMbN2QwRdmJOt/FWs3tsJNevRJbFUc3eb+vM9JoZlxDbrJWtlCW8KluMZI6vqa+zfy9129OY0l1IlvrkyVgrLXjPxcxyY5dJamYdmrXHSxjXrCNLGl/KEuuJemWLi5njfVY+W1nSBJl+j0FM6S6GrMxETHIzagOjS9NnSvzV4/k6y5lmxl20hhhTWSIPbTqTkqQk9xtKTbG7xWWLQZ2hdWqM3FUyvKtEN6GJcEbHBxzFnzkZy2WSW9bMO6u1kKIEdF5tQFnCbTzUpeU2JRQhmoEWly0Eh6ycMz9eoDig50+bxuq2YIOD57hnY27XILuqwVlkKXhMCZOyhLs4o6SWTc5lxu2i4SppsPhkGiuuu4pfTLH7zjo8/vKHWpbI4qmVvsy5uRKXq9myBQgMSwHUE4o8QdCmNqAs4U+Myu/fSv6MmMoW0aHi+fjlXqf5gu+xHIGffSxLpFcbaUgNreznf2MpW0ByjuO+LlvaVI4pwZ2KyAZFiMLXssSClc2pY6nF3iv5M2IpW0ByDaJHA+3VOo9VLum/t7JikvuVpBh9kNls8GUJuVfxDx2/1OFmWjDriqVsAck1CLnX6kJA5FDBz04lszxc0aR2VWd1cjV0oOTPWIYOCP4y/rcSmA1IZhuDLuIAQHIEN34mDgDBD8lBcpAcwQ/J4WdIDhD8df9mNSnyv2VsognJQXKQHMHPTA4/O5nMSHYAkiO48TNxAMlBcvgZkoPkCH5IDj9DciCW4Hdlp1uCG5IjDgCOxQYkM+KALzg2QEeAjXAsNkBHbARwbGshu7dezzk/rq8R3HyBsRHw3rGyI+z21LHsyz9FcAeno+wd+MIkndlkqydp/5fuUt9rkl1S3lh5bGUMkgOhOFZ2A76hv0un+ycEd3A6Spu/e+prkRkd/0eT7HEnie21STq2VdGnREgcgCAcK5n7sGb4TkguOB3zGmCPqQ6yFbr0j92W8zeXM7N84gB469hRk+zi2huxDULWcbrG+SnV4x/z/54PVZw0SYtK4gB47dh+XcrIkvUMJBekjpN1ZngLqsujHKKTi1JdxAHw2bG7rTywssUk3ZVesFwNUkfpvjaSOt6uie2W+v2Z6vMqNXubqDMDjDEOLlm5ozbZnzo/oHaURLIXknMLkqFnM6R2wuTXbyA5/3WUiw/PdWn62PzYtEYaZc9Z+WLlg0ka3BAHCaTpj1yd7lEyE72GldzOZoiwM4Yvgw86bTJJz9WdOa9JtjpGcKNjJDZqpIPaSOb4muo2njnfpsmkKSN8xrEENzpioxaikQ5qFzPH+5SbpK9sf+r8Dp3xNWUEdl4guNERG230WAd1hiZLUbmnUPrVdulPIboJXb7OmJyG481s4YxjsQE6YqONGushK+dMcj9pGgf0vJDgprW8MTM5gruMsZTZtwA/u2Wjsvxb2SgjQHIENzpiI6/HGiPJVQIRSC4OP8cSB5AcGZ7lKn5muQrJEfzM5AAzuSbfWB4ab8OxBDc6YqNQSU7uQq710Lg8b1fdNUOIUB4w7m7wc2+b5Jm9WijynBrBD8kBSK6h9bTgiJXFGgM4oUQkkB00TjXxuTetvDfJvS9ZFHpOjeCH5IBXNnK+g5rM9EaVtPIwvAqRriiZpVHoOTXPgr+6zdJXLQ2IPX+FAKLQccm0vhREIigBMtN6Z2rcabzKTG7eysGc1wo9p+aZY+e0HNCR0vW5Kb6vHCTnNvaYZLtzbOQ4jupyVbZubnZjv3o1uULPqQXg2O4SvgCQnNsYMP+VerCRo9ils5AOJZzxkt9/zc+pBeLY7wR30DpKfwepPUsp5qP6+6muTrCRAxBykSurPanjeVP/ainB3zj6dMlKcIer4139zvxmkgY2siK50YLZHSRH8DsH2eNfdo7tJ7iD1lHuLNiXObfVJBegsBEI1rGS0f82xbozQXLuQ2ZtSzUSHCQHgnXsbiW4PQR38DpKvflpznkpUzzBRiBEx8qTG3JLzRaCOwod5fag2znn5eb2q9gIhOZYaU0nReh2gjsaHeXe0qHMObl4J7cNcXUVBOfYh6Y1vSIhOXchXdrkwsNRPd6p54awEWilYxtpi9aqsZa5xxok56af05BnwU8q0a3oWAZIBKDVjm2kLRqzHPxMHADvHVsJJJAguTj8TBxAcpAcfobkAMEPyeFnSA4Q/JAcfobkQCzBX6Q7Uataz0Fy4fiZOABkeIIbPxMHkBwkh58hOUiO4Ifk8DMkBwh+SA4/Q3IgAMc63xaN4P4BK/h5VSxDB5AcNvAX69HSz2e0m/zNOUGkGZ4M7h8WTLKbMsiHdLv7hBnI8GRwfyHbVB0j3GviuJVZzECG32ict3I95/y4vkYGrw3ZXXfIo/FKP+EXJunjINsrTaivqug1yS4pb6w8NknbwiK4YPJ3IAZk+HXHS5PsEFyFfHGnyOCr4qySgg+QPsH3NC5FpDG61E2l52qP+lx2Bj6Q+p8+JcK14o5nSQAEnOEl6G/o77JbbNFmJrFkcCGHRU/GmkfGY0p0svJ4W2P1cTmTAJuBzOb3QgdkeFcgy5PDuozpLPheMWXw1zrjcR3TNc5PKdFJr93NOa/LDsJraVF5xMo7qIAM7xJGTXJFtLeE94opg8tM55YH45ysM8NbUKJ7lEN0Uq/tWuPM8XeogAzvCvpNUq+RJeuZgu8VWwaXWe8XkzSDcRmnrIykjrerz4WgO6w8U6J7lZq9TdSZAdbDLivfSlgRADJ8KZCm0g9M0nNVgv1FweCMMYOPmWIXatYLcvHhuS5NpTyRbV5z0cqckvYHs/YerNLD9xoUQIZ3AbIMmc2Q2gmz9npirBlcEsR8SUt937FfCbIDU5DhNxrSTPh+DRKWCwdruQUm5gzer0u99ojjvdqg+me++mR4MniYkFtnpiPWf0qXvIAMTwYHAJDhyeAAeIx/AT2ZPltThPXtAAADmHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3ViPjxtaT5MdDwvbWk+PG1yb3c+PG1pPng8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxOTI7PC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjIxRTs8L21pPjwvbXJvdz48L21zdWI+PG1vPiYjeEEwOzwvbW8+PG1zdXA+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1mcmFjPjxtcm93Pjxtbj4xPC9tbj48bW8+KzwvbW8+PG1zdHlsZSBkaXNwbGF5c3R5bGU9InRydWUiPjxtZnJhYz48bW4+NTwvbW4+PG1pPng8L21pPjwvbWZyYWM+PC9tc3R5bGU+PC9tcm93Pjxtcm93Pjxtbj4xPC9tbj48bW8+KzwvbW8+PG1zdHlsZSBkaXNwbGF5c3R5bGU9InRydWUiPjxtZnJhYz48bW4+MjwvbW4+PG1pPng8L21pPjwvbWZyYWM+PC9tc3R5bGU+PC9tcm93PjwvbWZyYWM+PC9tZmVuY2VkPjxtcm93PjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjI8L21uPjwvbXJvdz48L21zdXA+PG1vPj08L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtc3VwPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtZnJhYz48bXJvdz48bW4+MTwvbW4+PG1vPis8L21vPjxtc3R5bGUgZGlzcGxheXN0eWxlPSJ0cnVlIj48bWZyYWM+PG1pPmE8L21pPjxtbz4mI3gyMjFFOzwvbW8+PC9tZnJhYz48L21zdHlsZT48L21yb3c+PG1yb3c+PG1uPjE8L21uPjxtbz4rPC9tbz48bXN0eWxlIGRpc3BsYXlzdHlsZT0idHJ1ZSI+PG1mcmFjPjxtaT5iPC9taT48bW8+JiN4MjIxRTs8L21vPjwvbWZyYWM+PC9tc3R5bGU+PC9tcm93PjwvbWZyYWM+PC9tZmVuY2VkPjxtbz4mI3gyMjFFOzwvbW8+PC9tc3VwPjxtbz4mI3hBMDs8L21vPjxtbz49PC9tbz48bXN1cD48bW4+MTwvbW4+PG1vPiYjeDIyMUU7PC9tbz48L21zdXA+PC9tYXRoPo6OmFsAAAAASUVORK5CYII=)
this is known as an indeterminate form, because it is unknown. One to the power infinity is unknown because infinity itself is endless. Take a look at some examples of indeterminate forms. To solve this limit we will use the following formula -
![Error converting from MathML to accessible text.](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAnQAAAAaCAYAAAA+CMHMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAVrfl2dQAACN5JREFUeNrtXX1kXlcYP6IiIkpUVVSFiJqqCVFRUVGiJipiTPSPqipTM1EzqqaqItTUTNWYmoiZElWRv0ZU1dSMiqqqGlM1UVWiYiKivLuP9zne896ec+653/fc9/fjSHLu+XrOffKc333OlxAAkC/6gtAIwocOlcs13RVOd6KAtmddV5YyFtkPAAAAAAA4osEh6XNf5JoKwismNY2E8mXZFweDMBuEpSD8k3NdWcvoq04AAAAAQC1xnAfmhYSD92YQtj2R6y3H9ceUP0zCKP3vGbRxIwjLlv7Nqq48ZMyyHwAAAAAASIlfeGA+kIDQNUKhynI1DO0Np1vkv88pZX0ZhJuOBDcJbOW51LUvCA+DsCua3r7/QnnykhFeOgAAAKC2qOJ6rLSDclrCURW5XOLo/dH051YQBoNwKggroTxzBRI6l7p+4jRfBWFUU15eMs4JEDoAAACgpihrPVaa9m7WlNBtOhK6cLoxjn8ShLUg9ISezxpkXhN6T2CDnyXp31mH/n3DaXoN5WUpY9w0AAAAAOAdylyPBUKXHaEjXOdn1wsgMmkJXdQmj7xkBKEDAAAArOh1JBpp8nzN6Y87xhPKWquUN/HBlGs7ephkP+FnY6HnVZty3eI0XRZCl4eMmHKFnc3DzgJ+6wh0BkhNEpLkucZ5DjvGl7VWKU+k2RRBeMXPJiumQzq5dHLo0t0LwskgDPG7e8XvMi8SG4cw3xbN3bpvlbhfOc1nQfiRf98tQEbfNkV0i6ZXHKi2nQX81hHoTAzsiOYUS1dNFehbfmEjofgjQXjE8ocVxJQnjbLp4staq5Qn4hxbotslOh6EddGa9rvLP8/wc/JO3krYtj1Mnqm8VdH0kBIGgvANx1+IIZfunYbTkff0vPL8PD9fVOqmvx9kaCxNu4V1denSESl7EYTXSnu3cpYxy34QIrsd0yb7+LNSNpHXo7CzlbWzWSPqvEeMxfF0pKgyytSZrAmxts3DHPnMUsAgG9nHHiqQ3CGqW0C+bugcWx4XjHD+yw7xZa1VyhvSw7Mvg7IGmExsMVFYdVT6eUM8eaQ+UYjiAv8c5jQnxMfThXHliiN/kcYkSV3jnOdezjIW6aV0hck+yh3lM4qN3J+gHNjZYuxsoYNqxrrWCTpSVBll6kwhtnxG8YKY8Dmn+c1DJbLNkUsydTBGnjidvesQX9ZapaL+ebNqxyWl7/Y6pD9lMI4N9hhI3DEQ40ZKuVzTXeY04wW8k7h1vWePAR3yvKIhLFnKmEc/5EmUqdyXMdLDzpZrZ7MGvfsfMtaxTtaRIssoS2cKIXTXIpjpNc3XiPcsVtinpXR55MB/JxS/YohfMNQbji9rrVJasvZ9EN7xgP9EpHOhu2Av94tcb6hiSZinGsPvRjUGQ6J9SneJ46f4fQB+I4v/A5197Oe4qynLgZ0tzs5WWcc6XUcEk/0lHs92eFzcrzgt6qAz5GR4pMhwV0NMabnPAyXNpbj9Ka8JmjFkWtYo0YxnSrSRwNCE89Di56eifS2X9IQ9F+7r2MLxRa9VehdBfkz9JUFr/f7S5Hmd83ukadZzojX1OuDwz0PtWg/F02D8lmWc4/cqv44lub4BLgRCZ7CPukF1KkE5sLPF2tksbWBehK5TdYScFW80sr0QrXWXvuvMtELiJvljcFu0llTtVcpRZ0Kk17bPVff+5shDlsa8dEhTZSX6N8FXpS7PMJMJOlrkC1Y2+l23O2bKUPaURWmKWquUBgtKG4ncnVDq7M2pTpraOMu/n+G6lh36YUEAIHTpIO2jOl14VeinEF3KgZ0t385W1UPXqTpym5+R/HKmh+S7ZfgI8FFnGtwuFceYzEkZv7Pkveiie7Ru6wMLb4JLmk4xNCqhkOGsIV0cpSlyrVIadHFbd0XrMvoepW3d4BBAjQidyfaFvehJy4GdLdbOVpnQdbKObPCzUYf+9VVnqNzTmvgx0VpH/6eFxD9y0T15/MVDS0Nc0lRdiTYSGBqb+1ROOa5b0iRx6xaBNK7jMUue5+APQM0Incn2xdV32Nlq2dkqTrl2so58EO5nZvqqM6alGSc5n1wf/tiQ95KL7klGu2RpiEsaX416kjNpzoZe4hlDunlDGfPC35Pw5RfMCrgC0AGETtq+RSVuP8ddSVAO7Gz97GxWhK6TdUTejhReUtQn3DbS+KAzcuyUmxvJ2yrPPaX13tNKP0jyJ9eBb7r2p5yjvmhpiNx5uSb8POxQbnMei6FgpjyHudN3mM3TT3KXDhvKrsPWaBWjSvunRH0PvwRA6FT7qB40LRcpTyYoB3a2fnY2K0LXyTpyX7SOYuln2SZE0wse7l+fdYYIGh039li0vIjqZodD/I6fKnLPxdG9+8LuQqRB+6bQ7+hyuVPUhmlhnuOWuKjUe0FRYtoRQqdFk6uW3JVDljJsBxGa/hl1eXoUBZP/dHLN2jPRvpNmxPAVP5Lg675qWLfoCgDUidDd1+j2vIi+1s5UDuxsfexs1I0sYY8RdMSsIyOiNeWoBtknOxib3ezbZoQS9bDh+kO05rl7lI6NulPUhiGlngFDY59zOlWZJkT7GVBd/Pd5S13yqpDRGAY/nEeedRPeXSnn7O84lOvbPZU6HOAvqW2NrgBAnQjdpka36e83CcuBna2Pnc2a0HW6jkywbETs3rPHUp73+B5jcy727SNE3SlKmBXRiwlfa754w7s1PxXN88N0B8t2iXyuFUpzAfCwYzwAAH4YvG5RzqJ02Fl/7exoQUTBdx25xwRYtpuOBJLHda1ibC6G0BFsd4raMOzwVRA+RXlNydOvxA86CNYr7AsMs8gjDzMcc4wHACA/7IRCGiyW/BUPO+ufnZUeph3oSOT73jYQTIo/hrE5N7vWhqg7RW04Lezz9tOidYLypGidsjyuvGxyvco7PgcxfgEAkBNoQKODQftKqBt21l9MQEecQO2l3bvyOkmqjzx0R6BCxSHqTtG0OCqai/BXRfstBHtYCWmunnadYbclAACws7Cz0BHoCJAAUXeKAgAAALCzAHQEyBH/A6Er+GhNAzE0AAAL83RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaSBtYXRodmFyaWFudD0iYm9sZC1pdGFsaWMiPkw8L21pPjxtc3ViPjxtaSBtYXRodmFyaWFudD0iYm9sZC1pdGFsaWMiPnQ8L21pPjxtcm93PjxtaSBtYXRodmFyaWFudD0iYm9sZCI+eDwvbWk+PG1vIG1hdGh2YXJpYW50PSJib2xkIiBzdHJldGNoeT0iZmFsc2UiPiYjeDIxOTI7PC9tbz48bWkgbWF0aHZhcmlhbnQ9ImJvbGQiPiYjeDIyMUU7PC9taT48L21yb3c+PC9tc3ViPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+JiN4QTA7PC9tbz48bXN1cD48bXJvdz48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiIHN0cmV0Y2h5PSJ0cnVlIj4oPC9tbz48bXJvdz48bWkgbWF0aHZhcmlhbnQ9ImJvbGQiPmY8L21pPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+KDwvbW8+PG1pIG1hdGh2YXJpYW50PSJib2xkIj54PC9taT48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPik8L21vPjwvbXJvdz48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiIHN0cmV0Y2h5PSJ0cnVlIj4pPC9tbz48L21yb3c+PG1yb3c+PG1pIG1hdGh2YXJpYW50PSJib2xkIj5nPC9taT48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPig8L21vPjxtaSBtYXRodmFyaWFudD0iYm9sZCI+eDwvbWk+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4pPC9tbz48L21yb3c+PC9tc3VwPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+PTwvbW8+PG1zdXA+PG1pIG1hdGh2YXJpYW50PSJib2xkLWl0YWxpYyI+ZTwvbWk+PG1yb3c+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4oPC9tbz48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPiYjeEEwOzwvbW8+PG1pIG1hdGh2YXJpYW50PSJib2xkIj5MPC9taT48bXN1Yj48bWkgbWF0aHZhcmlhbnQ9ImJvbGQiPnQ8L21pPjxtcm93PjxtaSBtYXRodmFyaWFudD0iYm9sZCI+eDwvbWk+PG1vIG1hdGh2YXJpYW50PSJib2xkIiBzdHJldGNoeT0iZmFsc2UiPiYjeDIxOTI7PC9tbz48bWkgbWF0aHZhcmlhbnQ9ImJvbGQiPiYjeDIyMUU7PC9taT48L21yb3c+PC9tc3ViPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+JiN4QTA7PC9tbz48bXJvdz48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiIHN0cmV0Y2h5PSJ0cnVlIj4oPC9tbz48bXJvdz48bWkgbWF0aHZhcmlhbnQ9ImJvbGQiPmY8L21pPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+KDwvbW8+PG1pIG1hdGh2YXJpYW50PSJib2xkIj54PC9taT48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPik8L21vPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+LTwvbW8+PG1uIG1hdGh2YXJpYW50PSJib2xkIj4xPC9tbj48L21yb3c+PG1vIG1hdGh2YXJpYW50PSJib2xkIiBzdHJldGNoeT0idHJ1ZSI+KTwvbW8+PC9tcm93PjxtbyBtYXRodmFyaWFudD0iYm9sZCI+LjwvbW8+PG1pIG1hdGh2YXJpYW50PSJib2xkIj5nPC9taT48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPig8L21vPjxtaSBtYXRodmFyaWFudD0iYm9sZCI+eDwvbWk+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4pPC9tbz48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPiYjeEEwOzwvbW8+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4pPC9tbz48L21yb3c+PC9tc3VwPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+JiN4QTA7PC9tbz48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPiYjeEEwOzwvbW8+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4mI3hBMDs8L21vPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+WzwvbW8+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4mI3hBMDs8L21vPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+JiN4QTA7PC9tbz48bWkgbWF0aHZhcmlhbnQ9ImJvbGQtaXRhbGljIj5pPC9taT48bWkgbWF0aHZhcmlhbnQ9ImJvbGQtaXRhbGljIj5mPC9taT48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPiYjeEEwOzwvbW8+PG1pIG1hdGh2YXJpYW50PSJib2xkLWl0YWxpYyI+TDwvbWk+PG1zdWI+PG1pIG1hdGh2YXJpYW50PSJib2xkLWl0YWxpYyI+dDwvbWk+PG1yb3c+PG1pIG1hdGh2YXJpYW50PSJib2xkIj54PC9taT48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjE5Mjs8L21vPjxtaSBtYXRodmFyaWFudD0iYm9sZCI+JiN4MjIxRTs8L21pPjwvbXJvdz48L21zdWI+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4mI3hBMDs8L21vPjxtcm93PjxtbyBtYXRodmFyaWFudD0iYm9sZCIgc3RyZXRjaHk9InRydWUiPig8L21vPjxtcm93PjxtaSBtYXRodmFyaWFudD0iYm9sZCI+ZjwvbWk+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4oPC9tbz48bWkgbWF0aHZhcmlhbnQ9ImJvbGQiPng8L21pPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+KTwvbW8+PC9tcm93PjxtbyBtYXRodmFyaWFudD0iYm9sZCIgc3RyZXRjaHk9InRydWUiPik8L21vPjwvbXJvdz48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPj08L21vPjxtbiBtYXRodmFyaWFudD0iYm9sZCI+MTwvbW4+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4sPC9tbz48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPiYjeEEwOzwvbW8+PG1pIG1hdGh2YXJpYW50PSJib2xkLWl0YWxpYyI+TDwvbWk+PG1zdWI+PG1pIG1hdGh2YXJpYW50PSJib2xkLWl0YWxpYyI+dDwvbWk+PG1yb3c+PG1pIG1hdGh2YXJpYW50PSJib2xkIj54PC9taT48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjE5Mjs8L21vPjxtaSBtYXRodmFyaWFudD0iYm9sZCI+JiN4MjIxRTs8L21pPjwvbXJvdz48L21zdWI+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4mI3hBMDs8L21vPjxtcm93PjxtbyBtYXRodmFyaWFudD0iYm9sZCIgc3RyZXRjaHk9InRydWUiPig8L21vPjxtcm93PjxtaSBtYXRodmFyaWFudD0iYm9sZCI+ZzwvbWk+PG1vIG1hdGh2YXJpYW50PSJib2xkIj4oPC9tbz48bWkgbWF0aHZhcmlhbnQ9ImJvbGQiPng8L21pPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+KTwvbW8+PC9tcm93PjxtbyBtYXRodmFyaWFudD0iYm9sZCIgc3RyZXRjaHk9InRydWUiPik8L21vPjwvbXJvdz48bW8gbWF0aHZhcmlhbnQ9ImJvbGQiPj08L21vPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+JiN4MjIxRTs8L21vPjxtbyBtYXRodmFyaWFudD0iYm9sZCI+XTwvbW8+PC9tYXRoPkniqbMAAAAASUVORK5CYII=)
![Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus 5 over denominator x plus 2 end fraction close parentheses to the power of x plus 2 end exponent equals e to the power of left parenthesis space Lt subscript straight x not stretchy rightwards arrow straight infinity end subscript space stretchy left parenthesis fraction numerator straight x plus 5 over denominator straight x plus 2 end fraction minus 1 stretchy right parenthesis. left parenthesis straight x plus 2 right parenthesis space right parenthesis end exponent
e to the power of left parenthesis space Lt subscript straight x not stretchy rightwards arrow straight infinity end subscript space stretchy left parenthesis fraction numerator 5 minus 2 over denominator straight x plus 2 end fraction stretchy right parenthesis. left parenthesis straight x plus 2 right parenthesis space right parenthesis end exponent space equals e to the power of left parenthesis space Lt subscript straight x not stretchy rightwards arrow straight infinity end subscript space stretchy left parenthesis 3 stretchy right parenthesis space right parenthesis end exponent space equals space e cubed](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUsAAABYCAYAAAB8gtUfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAthfvO6wAADUVJREFUeNrtnX+kVlkXx5dHklwxriTJkCQZI5IruUYkI8mIMfJKRiQZuV4xkrySYYxx/7iuy8gYYySujDGSGGMkSYy8riSR0R/vH4kkSR6X+56vsx5zOrPPPmef5/za+3w/bHruOU/P3mftvc5aa6+9twghpGm+iMp84G2c03YSQkgp9kTlQVRWBd5OtO+/UZmiyAkhrgyi8jAqu3vS3l3a3gFFTwhx4XRUfm3w91YMpWmu0R0nhLjySN3wKpXhONebYErbTQghhV3Sx5bra6LyZ1Q26OcJ/TzhubIcvSR2swsQQopwXuIZYhv7o/Kz/vvrqHxegWU5lHii5XiLbZ+Nyjl2ARI6K4lBdycqW/lISoHY3ZEC912Oytmo3MuRR9F45ECt2t+jcqylth/R9hPivTIsAgYdJiju85GVdkW3F7hvp8rkYIWyA5MSpyy1wTaJZ8UJ6RS3o/JhQsHdjMr7FQ048JaPuBRvpFhuJWbLL6qFWaWyXC32mGmdoN2v2QX8ApaRzysn5rQNNg5F5ar+e7aA6+cy4D6Kyq2Wn8HRgorERwv+cKJtixLHMKuQ3bqofC/txi2HHZXrZf1t12tBMy1xoHtVhwaPS+xp9IZeUqVlA+2csXS+Mr+9UeKY5ZYWn9naqDzRwT+uhdw1ZblWZTuZeN4IeawZ8zeXo3K3xkEPF/uC9rmy7bfJtcqxZoq7T+hvm7IObNeCBcL4S+J4kE+WhokPtC0TORboI3W9qqgHBsR1HcBtckqtZZd2vPFc3l3np6iclPHSmGxyrfLZZsXdZ7UOJmzXguRSVBY6NijGGTxz2iYT+9UNR0B9fQX1gIK8UeNb34VrGmYo2o42V670RVkWbd9KQbnWkW+aJh13PyTZs/W2a8EBhfEyKpsK3HtC4vw2k7I90SFlCQX2yqAMN0scU5zQN+ilCuoBRbm9I7J8rl6CSztWPFEmfVaWablWnW+axBR3h4J+kXG/7VpwnFdXoSj3E281UUHN1zAoxh08CNhfSHyGy31bXebR5yriLV1YXzxiWOJ5dl1ZrrRcXOpTl7I0ybXqfNORkZEVd3/rYIkGC9zRaYf7P07ET/CG+71GN3yoFiKst387Kra90r81tyEqS1qWZrlWnW+aF3fvvbLcpia+K7+puY4ZvskSlpfLGxkz3LvUSiyauDziWYdcZLrhVJZVueGgynzTvLg7XO2XJa4FBVzoKyW+N6Nvuw8bHhQHxC2P8UqBeE5IuE7wgNfS/iw+leW71+fl3dBWWq5V55vmxd05wRPxo7hP++/VhwNX/GgLg8LF5D+hbewLmLT61sHCF3XjXqmFkMyxQ1z6tpTLY4QVhI0hFvQFl5QH+s0+xxBCnQqs7nX9RT2poeE7JrnWlW9qqyNThzRGcdDh/i1q/kNgo5SFyRKCKQtyKJ843P+xvjX7wrjJy1tVQWLy66r8PRmWxbSYsyAuqKWC60+j8p3EE24j62VKQytJkO85qEFRFaHtdf15yx3rTkq3waT0RCxkfcF716vimUyZ4D/V1IGRGrFHO/JAFR8Ec8RR0M+lXxxV5TTO95cKeg3vqUWWtmaTMtqkMkinaX2S+ryU4wq2kV/YFGj3w5rlWpYFS1/IvBZiTKXo23y1Ki9TLuZVVWRV86nEGxtgOdoLjc24bpA6kO6sUPGFMxJPpO3I8ESyJunOptzG5CCfU1f/S5XJPoMrvmhQoGmazi9siuC2aMt78C8CbFMIDIW4hDn+0Jfj9QJeByzLuwbLEt+bUXd8lJa2TZUmlIJp30go0m8K1LHp/MImwHMJavNfX7aop7LsXxurYI0qvs36GfHLm2KfOMiKWZZhpxTLi206v7AJnkhgx0qs5Fzr0jpbKpIw27hBLTPE1p5K/u5KvvGggNJoMr+wCfDCedi3QUfLkm0sUpeyCfoY0JgEOayfd0h7O3vXxSmxx+6azi9sgl8kwKNwqSypLNsE8bx0XAvu4+qAZDVQK8tkXbaRX1g3oyW5g74NupVA2+RDCV1ZYjBhSdn61N9eBTjQkIPZpU2o62K0UfWeEBtHy5KWZVtu+FTGvXcClRnc8fnA++W8BLzyhcqSyrItEKtbFEICGXRDD10iKks/gKt2j0OQhDLoEGfJWhbkevxqkh/EvqQL+zxiFQ2WHiXP0MFqCKzHRcLrdipL78HEx4z2HySDY7JnmsOSdHXQ2eJMWL71LGNwuh6/mgSpElj2N2W4hl3OsSxwtDoCv31aleSxlEKdpLL0mi360l1WxXmCQ5KESt7xq6dzFPKy/HMXmDOpzxf13vSmBbBGPjP85nKHn9doK7hXGuLA8/tXif+Hyx0J8QyX41fTlmXWcqj0bBoSlbFG/Y0qmxEb1QJNU8e2WFVxS8MaE4m23RG3PTRXCTfSIMQrXI9fTWKLWX6qFiNcbOzAsqj//6Iqia/UYr2SoRT/J3H8yxe3GHHeJYf78Vyes/sR4gdljl91AbHM4/LPdcK79O+fWaxZrABx2V6tyaNws3DZcxCbLdxgFySk+9R1/GpV/CDuZ9Q0dRSuiT3iloh9UttICCFjgRlz153OmzoKNw3WACPXcK/Dd65Kvw4sI4TUBCzeZyW+1+RRuABxVezOcsCxnohXbqeYCSFVUGYxf5NH4W5RRel68h7yXh9RvISQqsAW/d873N/kUbiwCpE6tbbE7yC8cI7iJYRUBdxobP+1qaCV19RRuJhEQgpUma26kIHwukTdCCHEyn8kf0a76aNwr0v5eCOs0YsUKyGkakaHuGfFINs4CrfshBA2E/lLenLwOyGkeRCL9H2Haih1TFhxNx5CSK0giXvB4/oHvfs0IYQQQgghhBBCCCGEEEIIIYQQQggh9fOFdO+Q+zmtFyGEdALsQPRAupecjvogaX6KIiKEtA3O6cE5Qbs7Wr9dWr8BRUUIaROcEfSr5XqZjXvzGP0/2B8TR0bk7Vt5je44IaRtHol9I+CVGn97oMr6fs59U8JNfQkhLbu4jwtYgXVT5PTGRx0OFRBCAue8xDPOecoS7jImWo7XUAec63OrwH3YpZ27oBNCWgGxwCMF3WVYoTjV8ZhFqbruRblR4pjllgJ1OKL1JYSQxoFr67IzOXZMf1DRb+OUyeuqMIve/5AiI4S0wRtxy63ERruPK/hdKEgcV7HO4Tuo52uKjBC/wYmHlz2st8vkDRQbToSsIm55Q8qdtTPsqBwuS/apl7ZrhPSK0Vk268ZURl1VlrhnOSp3Kxz0ZXM3V0rKoco6m3JDJ/S3TWcA2a4R0itwpMGs4+B+46Fl2fX62uRQ5bPIyg2dlezjLWzXCOkNmKE95DAAq1wJQ2VplsMaic8335Cw7v7Mse5cn0U6N/SQZM/W2661ga9hI5e6MzTSQZ6rC+gyALuipEJSlmk57Jf4KF/wdVQ+r/BZmHJDoaBfZNxvu9Y0PoeN0nVPhkaQB3wgcS9DIx1kWGIAdl1ZrnSguD63YYYFcTYq90q0MwtbbuhbB0u0LXwOG9nqjgnDpwyNUFnSsiynLHfqdw5W9CzyckN9UJY+h41sdR8YrHefQiN0w6ksW3PDAXZTuijFYlx5zyIvNxSu9ssS19hfx687FkvMG0ItvoRGeoPrmxq8luIrV6gszfWdl3d3dk/L4XBCSS5KHMMc51nk5Yb6YsX47AkNLZbvMY+t/aw2mWKxXoM0km9zGp12ZeAWvtK3WzJnD7O3t/XvruCNi40mFlIP94TE8Zl9jgOnqc5QZD9LU33TrmFSDngWS2pxjKzC+yWfa54sR/gSHwtNWYpa+19F5WQgyjKJKRbrLeMmQ29VBYmlhFcljovZmFYFmOaCPthpfbjfSbziZmQNYU/IXanvIHBfxw7k4+Ysmshb7lh3UroNn2ZeQ3TDs5SfL6GRvDESVLjgqCqncb6/JMVyv95TayxtzSZ3D9qkHetS6p5PUp+XJH/ZYRs5i1lv2Ic1y6EsCxbZLUi3cvp8DhvZ6j6t/dLH0EgWWbHYXnNG4h2AdhiuXZfs9JazKTc0qTTm1NX/Ut9O+wyu+KJBgZpoOmfRBLdoqwafw0bpuo/qiJftzai872loxCaLY+yyf/NBVP5QNxyKcX0By/KuocPjezPqjk/r37ap0ryW8dChSL8pWM+mcxbTzAk3/+172Mil7iEkpdtisb1jjSq+zYmOeDPnTZ3V+cqwU4qfbdN0zmIadG4eK9HvsJFL3X0KjeTx1peKblDL7K2+AT8KbOA8KKiEmsxZNL0guPFvd/prW2GjPsrIFIvtrBmMN+hh/bxDqtspvCuckvxYYNM5i2l+kf4chVt2KWhT/bXNsJGPMikjo7xYbCdBPO+c4c25OqDBOVCrLcu6bCNnMcletWIGQtrur22HjSijDiuRl6k350BdhdAGLoLpWCmwqmP1WqWKeg/HGPsrZdRtBWKygO4EKki44/Mdq9O89G9nmLIuX9/6q49ueLAyQkxhkf2EsL8SysgOXL97lC9hfyWUUT6Y+JjReAJm9RCYnabMCfsroYzeBStLsFphWRvJWT3C/kooI+X/iqwZr1SBnPsAAAdsdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPkx0PC9taT48bXJvdz48bWk+eDwvbWk+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjE5Mjs8L21vPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj4mI3gyMjFFOzwvbWk+PC9tcm93PjwvbXN1Yj48bW8+JiN4QTA7PC9tbz48bXN1cD48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bWZyYWM+PG1yb3c+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+NTwvbW4+PC9tcm93Pjxtcm93PjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjI8L21uPjwvbXJvdz48L21mcmFjPjwvbWZlbmNlZD48bXJvdz48bWk+eDwvbWk+PG1vPis8L21vPjxtbj4yPC9tbj48L21yb3c+PC9tc3VwPjxtbz49PC9tbz48bXN1cD48bWk+ZTwvbWk+PG1yb3c+PG1vPig8L21vPjxtbz4mI3hBMDs8L21vPjxtc3ViPjxtaT5MdDwvbWk+PG1yb3c+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxOTI7PC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjIxRTs8L21pPjwvbXJvdz48L21zdWI+PG1vPiYjeEEwOzwvbW8+PG1yb3c+PG1vIHN0cmV0Y2h5PSJ0cnVlIj4oPC9tbz48bWZyYWM+PG1yb3c+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbz4rPC9tbz48bW4+NTwvbW4+PC9tcm93Pjxtcm93PjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj54PC9taT48bW8+KzwvbW8+PG1uPjI8L21uPjwvbXJvdz48L21mcmFjPjxtbz4tPC9tbz48bW4+MTwvbW4+PG1vIHN0cmV0Y2h5PSJ0cnVlIj4pPC9tbz48L21yb3c+PG1vPi48L21vPjxtbz4oPC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+eDwvbWk+PG1vPis8L21vPjxtbj4yPC9tbj48bW8+KTwvbW8+PG1vPiYjeEEwOzwvbW8+PG1vPik8L21vPjwvbXJvdz48L21zdXA+PG1zcGFjZSBsaW5lYnJlYWs9Im5ld2xpbmUiLz48bXN1cD48bWk+ZTwvbWk+PG1yb3c+PG1vPig8L21vPjxtbz4mI3hBMDs8L21vPjxtc3ViPjxtaT5MdDwvbWk+PG1yb3c+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxOTI7PC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjIxRTs8L21pPjwvbXJvdz48L21zdWI+PG1vPiYjeEEwOzwvbW8+PG1yb3c+PG1vIHN0cmV0Y2h5PSJ0cnVlIj4oPC9tbz48bWZyYWM+PG1yb3c+PG1uPjU8L21uPjxtbz4tPC9tbz48bW4+MjwvbW4+PC9tcm93Pjxtcm93PjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj54PC9taT48bW8+KzwvbW8+PG1uPjI8L21uPjwvbXJvdz48L21mcmFjPjxtbyBzdHJldGNoeT0idHJ1ZSI+KTwvbW8+PC9tcm93Pjxtbz4uPC9tbz48bW8+KDwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbz4rPC9tbz48bW4+MjwvbW4+PG1vPik8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4pPC9tbz48L21yb3c+PC9tc3VwPjxtbz4mI3hBMDs8L21vPjxtbz49PC9tbz48bXN1cD48bWk+ZTwvbWk+PG1yb3c+PG1vPig8L21vPjxtbz4mI3hBMDs8L21vPjxtc3ViPjxtaT5MdDwvbWk+PG1yb3c+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPng8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxOTI7PC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjIxRTs8L21pPjwvbXJvdz48L21zdWI+PG1vPiYjeEEwOzwvbW8+PG1yb3c+PG1vIHN0cmV0Y2h5PSJ0cnVlIj4oPC9tbz48bW4+MzwvbW4+PG1vIHN0cmV0Y2h5PSJ0cnVlIj4pPC9tbz48L21yb3c+PG1vPiYjeEEwOzwvbW8+PG1vPik8L21vPjwvbXJvdz48L21zdXA+PG1vPiYjeEEwOzwvbW8+PG1vPj08L21vPjxtbz4mI3hBMDs8L21vPjxtc3VwPjxtaT5lPC9taT48bW4+MzwvbW4+PC9tc3VwPjwvbWF0aD6qnKy4AAAAAElFTkSuQmCC)
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
Related Questions to study
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
The basic problem of this indeterminate form is to know from where tends to one (right or left) and what function reaches its limit more rapidly.
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
The correct relation is.
The correct relation is.
A vessel whose bottom has round holes with diameter of 0.1 mm is filled with water. The maximum height to which the water can be filled without leakage is
(S.T. of water )
A vessel whose bottom has round holes with diameter of 0.1 mm is filled with water. The maximum height to which the water can be filled without leakage is
(S.T. of water )
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
A capillary tube at radius R is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is M. If the radius of the tube is doubled. Mass of water that will rise in the, capillary tube will now be
A capillary tube at radius R is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is M. If the radius of the tube is doubled. Mass of water that will rise in the, capillary tube will now be
Direct substitution can sometimes be used to calculate the limits for functions involving trigonometric functions.
Direct substitution can sometimes be used to calculate the limits for functions involving trigonometric functions.
If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm then the surface tension of soap solution will be
If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm then the surface tension of soap solution will be
The quadratic equation whose roots are I and m where
is
The quadratic equation whose roots are I and m where
is
Two bubbles A and B (A>B) are joined through a narrow tube than,
Two bubbles A and B (A>B) are joined through a narrow tube than,
Direct substitution can sometimes be used to calculate the limits for functions involving trigonometric functions.
Direct substitution can sometimes be used to calculate the limits for functions involving trigonometric functions.