Maths-
General
Easy
Question
![1 half](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJFJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYLsAbiNUD8CYh/QaujaHIMOgjEkUDMA+VrAfFRqBjFQB6IL1HLyz+oYYgl1HsUAQ4gPgmNBLKBIBBvAGI3SgxRghqiQokhGkA8G4i5KDFEHIhXATELpYG7BeoimhZyWAEAI3M1I31CbrEAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MjwvbW4+PC9tZnJhYz48L21hdGg+ND6jrQAAAABJRU5ErkJggg==)
- 2
- 4
![1 fourth](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAGxJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYr8KFGDPEA8TVqGDQTiJMpNcgaiPdSWiaxAfElIJan1KAOIM6htJTUA+Kj1ChuTwKxCjUMommOH2J1GwCVNzk6FQ24cQAAAGJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1uPjE8L21uPjxtbj40PC9tbj48L21mcmFjPjwvbWF0aD7CA6ZrAAAAAElFTkSuQmCC)
Hint:
We can apply L'Hopital's rule, also commonly spelled L'Hospital's rule, whenever direct substitution of a limit yields an indeterminate form. This means that the limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.
In this question, we have to find value of
.
The correct answer is: ![1 fourth](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAGxJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYr8KFGDPEA8TVqGDQTiJMpNcgaiPdSWiaxAfElIJan1KAOIM6htJTUA+Kj1ChuTwKxCjUMommOH2J1GwCVNzk6FQ24cQAAAGJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1uPjE8L21uPjxtbj40PC9tbj48L21mcmFjPjwvbWF0aD7CA6ZrAAAAAElFTkSuQmCC)
![Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction](data:image/png;base64,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)
We first try substitution:
= ![Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of 4 minus 2 over denominator 4 minus 4 end fraction space equals space 0 over 0](data:image/png;base64,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)
Since the limit is in the form 0 over 0, it is indeterminate—we don’t yet know what is it. We need to do some work to put it in a form where we can determine the limit.
( L 'Hopital's Rule for zero over zero;
)
(
)
Let ![y space equals square root of x space end root space s o comma space y rightwards arrow 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIQAAAATCAYAAABRJ6VcAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAvhJREFUeNrtmU9oE0EUxpdQSilBlFiKRFCKB5EighaVKl5EikjoQVEREdGDeApeFFQURCoe4kEvUoMU0UDxTxGpBxGRUEQRFRERRcSDeOjBIqJF6p/vySdMht3s7O5sNg37wY8mM5PdmTdvZt6bOk7zKwv+WCbVLNYO8CA1Q6r/ugv2p2ZIJZoPvvBvqlTOAXArNYM19YPr4Cv4CV6AXbNpABI7bE3n0Zoegp0M1EXLwATLml6LwSToSOcxVi0CL/XCMtju0rgITifU0SNguE79PnDGpfwU68LqKPgIZpiiHtbqu2ivb2AajIR0Wps2Pw6WRBjztF6wB5zVyjrBW5AzeGAcuf9zMODT5hnoVr7vBRciOoM4YbtH/TyuJnlPBswBFRfbmSiqzVVVGBeE2frX8tio0WYwqpWdoOfFraxLWS/4DNp8fisOU+LnjeB+xL5M8Dlekgk8pJX1cBKDyqbNZVE85cIbDrBjSbvHDDZrJB75StsW38d8fssWd5mDWKfVDYFzhs+5BzYwYs5F7NM27joFl7qMR0wj36dCvCuozYPcxI4avF92uzGwyavBd+VziWeZqcIcGcfoEHLP8ESr+wBWGb67yBRquSVHXQCqzHDU3Wsly3WtdsLfpEaxudcOcbHOkafuamN+cUeVDXvoqZkGBY8HwW8lFlgD3hkcF2peXbKcOnUwVtitlBU8Vl6UwNuWzYPEEEt5rHT6NRzhoK9qhmiEZKVc4+fz4KTBb8SItzmwLFdIzmKfytqljcQr4y7HyGsaOYxs2dw0y+imU5sstn+eXnbLSRugS+AHOzppYOAuTo7qAFvAFUv96eNEq8+Xvn3ie0R5cJOZiduKle17sMlsfieI8w5yEIUEHGIu+AVugEc+bds5EXmPiRgI2Ycpjn+GMYGb4dbTUSRmecP004ngEI22eaBrgYLBZMSpKjtWdFpDFaaW9ZS0zetqnJcUSamPDrGwBZxhBVPKtia3uad6eb4krVb5R1beqb1BbWab1+gvTyPTtEBZzAQAAADrdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnk8L21pPjxtbz4mI3hBMDs8L21vPjxtbz49PC9tbz48bXNxcnQ+PG1pPng8L21pPjxtbz4mI3hBMDs8L21vPjwvbXNxcnQ+PG1vPiYjeEEwOzwvbW8+PG1pPnM8L21pPjxtaT5vPC9taT48bW8+LDwvbW8+PG1vPiYjeEEwOzwvbW8+PG1pPnk8L21pPjxtbz4mI3gyMTkyOzwvbW8+PG1uPjI8L21uPjwvbWF0aD71fsZBAAAAAElFTkSuQmCC)
![Lt subscript y not stretchy rightwards arrow 2 end subscript fraction numerator y minus 2 over denominator open parentheses y close parentheses squared minus open parentheses 2 close parentheses squared end fraction space equals space fraction numerator 1 over denominator 2 cross times 2 to the power of 2 minus 1 end exponent end fraction space equals 1 fourth](data:image/png;base64,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)
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
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physics-
A medium shows relation between i and r as shown. If speed of light in the medium is nc then value of n is
![](data:image/png;base64,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)
A medium shows relation between i and r as shown. If speed of light in the medium is nc then value of n is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPIAAACwCAYAAAA1+DPDAAAgAElEQVR4nO3daVNUWZ7H8W8mJJAJCZlsJsi+KIuIqCiiIggiKKhlOVVWRNf0zER0RD+YiX4wz+cFzAuYmCWmuit6umrKdrdFUGQRF1QQkEUBZRcFMtm33O6dBz03A8ultEpBkvOJqAeFQF6WH+fec/7nf1SyLMsIgrCqqVf6AgRB+OVEkAXBDYggC4IbEEEGZFlGkiTEdIGwWq35IMuyjNVqZXJykvn5eSRJWulLEoT3tuaD7HA46O/v59SpUzx+/Bi73b7SlyQI781zpS9gJUmSxNTUFPX19Zw/f56FhQXCwsIwmUyo1Wv+b5ywiqzZICvPxd3d3ZSXl/Po0SMkSSIxMZHCwkI0Gg0qlWqlL1MQ3smaHXZkWcZms9HR0cGdO3cYGxujqamJlpYWbDabeFYWVpU1GWRZlnE4HHR0dNDU1MTExAQOhwOr1crjx4958OABi4uLYhZbWDXWZJABFhYWqK2txWw2s2vXLiIiIsjOzsbLy4vKykqmp6dFkIVVY00G2WazYTabGRsbY9OmTfzqV78iLi6O0tJS8vLyWFxcZHp6WsxgC6vGmpzsmpycpK+vj7179xITE4PFYsHPzw+DwcCePXtISEhgfHycgIAATCbTSl+uIPykNRlkHx8fwsLCCAoKws/Pj4mJCSRJQpIkDAYDISEhWCwWdDrdSl+qILyTNRlkPz8/4uLi0Gg0OBwO19tlWcbDwwOtVkt4eLhYSxZWjTUZZA8PD9RqNSqV6qUgK1QqFR4eHitwZYLw87jVkCPL8jvPNItiD8GduE2QJUnCZrNht9vFspGw5rz3rbXT6WRoaIihoSH0ej1RUVEEBASs6Ain1Ey3tLTg7+9Pamoq3t7eK3Y9grDc3ntEliSJ1tZW/vCHP3D16lVGR0dXfAS02+0MDAzwv//7v1y7dk1sRxTWnJ91a22z2ZiZmWFhYQGn0/mhr+m9yLKMxWKhurqahoYGampquHPnjiixFNaUV26tlV9+h8PhWltVqVSo1WrUajWyLLNx40a+/PJLAgMDCQoKAnA9my69xXY6na4ZYOXjX/d6TqfT9Vqenp4vzSa/y8cODw9TWVlJf38/w8PDVFVVkZWVhbe3t5h9FtaE1wZ5fn6egYEB+vv7mZubw9PTk+DgYOLj4/Hw8GBhYQF/f39MJhM6nY7FxUUGBwcZGhrCYDBgNBqZm5ujt7cXT09PoqKiiI2NxdfX95ULkGWZsbEx2tvbWVxcJC0tDa1Wy61bt1CpVGzatIno6Og3rulOTk7S1tZGe3s7ExMTqFQq2traePLkCampqeh0OjFDLbi9V4K8sLBAc3MzV69epaWlhYWFBWw2G5GRkfz6178mMDCQy5cv09DQQH5+PseOHUOv19PU1MT3339PcHAw27dvx2azce3aNWZmZti5cydff/01SUlJrhFXIcsyAwMD/Pd//zd9fX18+eWXhIWF8R//8R/Y7Xb+7u/+jq+++gqNRvPKxUuSREtLC42NjZhMJubm5tDpdOh0OqqrqzEajcTFxYlRWXB7rwxz09PT1NTU0NDQQF5eHv/8z/9MUVERarWaubk51q1bR3JyMuHh4czNzbnCk5SURFxcHF1dXbS1tREVFcU//MM/EBERQUtLC62trczPz7/2uTUkJITs7Gz8/f354x//SG1tLf/4j/9IbGysqwHAj8myjN1up6WlBbPZzMmTJ0lJSSEvL4+SkhK6uroYGRlZ8Wd4QVgOr4zIkiRhNpuZmpoiLCyMzMxM0tLS6OrqIjIyEqPRSHx8PP39/a6RztPTk8jISJKSkhgdHSU2Npbt27ej0+no7u7mxo0bTE9Pv7GKSrlNt1qtREZGUlBQQF5eHiaTiYCAgNcuJc3Pz9PT04PBYKC4uJjU1FRu3bpFeHg4eXl5aLVa7HY74+PjhIaGinJLwa29EmSdTsfmzZuxWCy0trbi4eFBYmIiycnJBAQE4OHh4apJVqlUrv9kWUaj0RATE+N6X7VajZ+fH35+fq6Pe53Z2VmGhoZQq9UcPXqUAwcO4OPjw86dOwFeG0Kn08ns7CxbtmwhOjqakZER1Go1TqcTPz8/jhw5Qk9Pj5i9FtaEV4Ks1+s5dOgQRqORyspK/u3f/o2oqChKSkrIyckhMDDwtZNHyoy1j48PXl5ervApb3/ThJMkSYyNjTE8PMzOnTtJTk5Gq9W6/lC8iVarJSkpCY1Gg5eXFyMjI64STQ8PD3Q6HYmJiW+c8RYEd/JKkFUqFQaDgezsbCIiIujo6OD27dtcuHCBsLAwtm3b9s6zwO/yfsqs9ZMnT9i5c6erSuynPtbT0xN/f3/UavUbb9mVW3Ixay24u5eCLEkSFouF7u5uvLy8SExMJDIykpGRES5dusTz589dXTNsNhsOhwOn0/nS2vP8/DxWq/Wl9eelJzn8+DZXlmWmp6d59uwZBoPBdUv+U95lh5IIsLBWvBRkWZYZHR3l+vXrPH/+nPz8fHQ6HZOTk0RGRuLv74/T6WRwcNDVbTItLY3IyEjMZjOPHz+mtbWVoKAg0tPTUavVDA8P09vbS1dXFxaLBYPB4AqgEvCJiQnsdjsmkwmDwSACKAjv6aUgq1QqfH198fX1paenh+bmZpxOJ7GxsRQUFJCamorD4aCnp4euri48PT3p7OwkPj4es9lMV1cXQ0NDPHnyhI6ODjw8PBgdHWV2dpbe3l6eP39OdHS0a01YlmUmJyeRJImUlBTCw8Nfu14sCMLbvRLk0NBQDh8+zKZNm5ienkaSJEJDQ0lISCA4OBhZlikoKCA2NhaVSkVMTAzr1q3DaDTyT//0T0xNTREeHk5ERAQqlYpf//rXFBYWYjAY2LBhA56eni+9nl6vp6CggMzMTBITE0XxhiD8DK8EWavVkpCQ4CrGgL8u/yg1zwBJSUls2LDBNUOsPAeHhIQgSdJLM8Umk8n1tqWfQ3k9nU5HfHy863XEbbUgvL9XZq2VEC4dOX/sQ97+qlSqt76WIAg/TSywCoIbEEEWBDcggiwIbkAEWRDcgAiyILgBEWRBcAMiyILgBkSQBcENiCALghtwqyCLTiDCWuUWQVb2Jmu1Wnx8fES9trDmuEWRs0qlws/Pj4yMDNatW4eXl9dKX5KwSvz4UIXVyi2CrFarCQkJ4auvvsLT0xMfH5+VviThE6ecUuJ0OvHw8Fj1G3dW99X/P5VKhUajISQkxPX/gvA6Slcapb3U1NQUkZGRRERErOomjW4RZOCdGvYJa5tyqMGzZ8+or6/nzp07TE5OcuTIEUJCQlb1/IrbBFkQ3kaSJBYXF+np6aGiooIzZ87w6NEjjEYjqampWK1WvL29RZAF4VMkyzI2m43p6WlaWlr44YcfqKurw2w2u04pyczMRKPRrNoQgwiy4OacTie9vb3U1NRw+fJlGhsbmZ2dZevWrRw9epR9+/YRExOzqm+rQQRZcENK//TJyUlaW1u5evUqlZWVPH36lJCQEPLz8yksLCQvL4+QkBA0Gs2qnugCEWTBzciyjMPhYGxsjPv373P69Glqa2uZnJwkJiaGgwcPcuzYMVJSUvD393ebrq0iyILbUJ6Hnz17xpkzZ/jjH/9If38/ABkZGfzmN79hz549hIWF4enpuepH4aVEkIVVT5ZlrFYrExMT3L9/n8rKSmpqahgcHCQoKIj8/HwOHTpEVlYWISEhq77443Xc7ysS1hRZlllcXKSzs5O6ujoqKiq4d+8eDoeD9PR0cnNzKS0tZfPmzXh6eq7qCa23EUEWViXlNnpkZIRHjx5RVlZGZWUlo6OjBAYGkpmZyeHDh8nKysJkMrl1iEEEWViFJEnC4XAwNDTE5cuXuXr1Ki0tLUxOThIREcGJEyc4evQocXFxGAwGt3oWfhMRZGHVUJaVZmZmaG1t5cqVK5SXl9PZ2YnBYODAgQOUlpaye/du12GBayHEIIIsrBKSJGG323n+/Dn37t2jsrKSuro6nj17hslkIi8vj5KSEnJyctDr9Xh4eLj1rfSPiSALnzxZlllYWKCvr4+KigrOnTtHS0sLnp6eJCUlcfz4cQ4dOkRiYiLe3t5rZhReSgRZ+KRZrVZmZmZ48OABly5d4saNG7x48QKDwcCOHTv41a9+xebNmzGZTKu+zPKXEEEWPknKhNbAwACVlZWUlZXR1NTE9PQ0ycnJHDhwgIMHD7J161Z0Ot2aDbBCBFn45EiSxPj4OG1tbdTW1nL27Fn6+voICAigqKiIgoIC9u/fz/r161f11sMPSQRZ+GRIkoTNZsNsNnPz5k3OnTvH/fv3mZ6eJioqitzcXL7++muSkpLw9fVFrVaLEP8/EWRhxSnLSrOzs/T09HDq1CnXbiWtVktubi7FxcVkZWURGxuLj4/PmpzQehsRZGFFKe13xsbGuH37tqtOemxsjLCwMHJyciguLmb79u2uOmkxCr9KBFlYMZIk4XQ66e7upra2losXL9LY2IjT6SQ9PZ2CggJyc3NJS0vDz89PjMJvIYIsrAin08nCwgL9/f384Q9/4NKlSzx//hydTkdOTg5/8zd/Q0FBAX5+fnh5eYlR+CeIIAvLSpIkrFYrZrOZ+vp6vvvuO1paWrBYLMTExFBcXExJSQmpqakEBASIUfgdiSALy2p+fp62tjYqKyu5fv069+7dw8/Pj71793Lo0CH27dtHQkKCGIXfkwiy8NEppzooddIVFRXcvHmT0dFRkpKS2L59O0VFRezatYugoCAxofUziCALH42yrDQ/P8/w8DA1NTV89913tLe3o1arSU1N5bPPPnONwsrasPD+RJCFj0aSJGZnZ7l//z5nz57l+vXrjIyMoNfrOXToEJ9//jlpaWkEBgau+r7SK00EWfjglC2HY2NjVFVVUV5eTm1tLfPz86SkpJCfn8/BgwfZsmULWq3WbTpZriQRZOGDUnpodXV1UVlZyZ///Gc6OzvRarXk5ORw5MgRDhw4QHh4+JrbM/wxiSALH8TSHlodHR2cOnWKGzduMDU1xfr169m/fz/Hjh0jNTWVoKAgEeIPTARZ+EWUCS2bzUZ/fz9lZWX85S9/4eHDh9jtdpKTk/niiy84cOAAcXFxaLVaEeCPQARZ+NmUZaWJiQnq6uq4cuUKd+/eZWBggODgYPLy8igsLGTnzp1ropPlShJBFt7b0t1Kg4ODNDY2cvr0aW7cuIGnpyeJiYkUFhZSUlJCRkYGGo1GTGh9ZCLIwntzOp3MzMzQ0NDAhQsXqK6uZnh4GF9fXzIzM/nqq6/Izs4mNDRUVGgtExFk4Z0pddLDw8PU19dz5coV7ty5w9jYGLGxsRQUFFBYWMiWLVvEhNYyE0EW3okkSSwsLNDR0UFZWRlVVVV0dnYyNzdHdnY2xcXF5OfnEx8fj06nW+nLXXNEkIW3Up6HR0ZGePDgAWVlZZSVlWE2mwkNDSUvL4+TJ0+yY8cOV520sPzEd114LSXAi4uLjI2NUV5ezpkzZ7h37x5qtZqoqCiOHz/O119/TUREhGi/s8JEkIXXUuqkm5ubOXPmDHV1dfT09KDT6di7dy8lJSXs2rWL6OhotztreDUSQRZcZFkGYHFxkZ6eHu7evUtNTQ21tbUsLCyQmppKQUEBu3fvZsuWLQQGBoq14U+ECLIA/DXEkiS5Dki7du0aFRUV9Pb2otVq2bVrF8XFxRw9ehSj0Sj6SX9iRJAFZFnG4XBgNpu5d+8e//M//8OdO3eYnZ0lIiKCkpISioqKSEtLIyAgQCwrfYJEkNc4p9OJ1WrlyZMnlJeXU1ZWxqNHj7Db7aSnp1NaWkphYSFxcXH4+vqKAH+iRJDXuMnJSRobG7l8+TJVVVU8ffqUiIgIcnJyKCwsZPv27URERIiN/584EeQ1SFlWevbsGXfu3OHMmTPcv38fm81GRkaG66zh1NRUfHx80Gg0K33Jwk8QQV5DlAmthYUFuru7uXLlChcuXKCrqwu1Ws22bds4efIke/bsISoqSkxorSIiyGuIw+HAYrFw9epVV5305OQkJpOJzz77jIMHD5KcnIzRaBS30quMCLKbWzoKd3Z2UlNTw5UrV2hpacHDw4OsrCxycnIoLS1lw4YNYrfSKiWC7OYkScJsNtPe3s65c+f4y1/+wtjYmGtCq6SkhKysLAIDA8Wy0iomguymlC2HQ0NDVFVVUVZWRktLCzabjbS0NI4ePUphYSHR0dEYDAZx1vAqJ4LsZpQyS4fDQXt7O6dPn6a6uppHjx5hNBrJzc3l2LFj7Nixg8jISNG5w02IILuRpRVaNTU1XL58mbq6OmZnZ0lISKC4uJiCggK2bt2KTqcTIXYjIshuYOmE1tDQELdu3eKbb76htbUVjUbDhg0b+OKLLygtLSUyMhKNRiN2K7kZEWQ3YLfbmZiYoKmpiXPnzlFZWcnExARGo5GcnBxOnjzJ9u3bxbKSGxNBXsWUw8KfPHlCRUUFNTU1PH78mNnZWbZu3UpBQQE5OTkkJSVhMBhQqVQixG5KBHkVUm6lX7x4QXNzM1VVVVy6dIlnz54RFhZGUVERxcXF7N2713U0i+DeRJBXmaV10jU1NZw7d46HDx+yuLjI5s2b2b9/v6u4Q6/Xi2fhNUIEeZVQRuG5uTl6enq4cOEC5eXldHR0oNfryc3N5ciRI65RWLTfWVtEkFcJh8PB2NgYtbW1XLx4kcbGRiwWC2FhYRw6dIhDhw6xefNmUaG1Rokgf8KUUdhqtdLZ2UltbS1XrlyhoaEBjUbD9u3bKSgoIDc3l+TkZLRarajQWqNEkD9RygFp4+PjPHr0iIsXL3LlyhUGBwcJCgpi586dfP755+Tn56PX68Wy0hongvwJkiQJh8PB8PAwtbW1fPvtt65THRITEzl8+DBHjhwhMTERf39/sawkiCB/SpRReGpqipaWFiorK6mtreXhw4f4+/tTVFRESUkJ27ZtIz4+XozCgosI8ifE4XAwNDTEzZs3KSsr486dO0xNTZGSkkJ2djalpaVs27YNPz8/MSMtvEQEeYUpR7NMTEzQ29tLVVUVFy5coLu7G19fX/bu3cuRI0fIysoiOjpabHYQXksEeYVJksT09DS3b9/m/Pnz1NbWYrFYMBqNHDx4kKNHj7J161ZXnbQgvI4I8gqRJAmn00l/fz8XL16koqKCpqYmHA4HGRkZlJaWkpOTQ0JCgriVFn6SCPIyUya05ufnefz4MRUVFZw5c4a+vj68vLzYt2+fqyn8unXrxNlKwjsRQV5Gsixjs9kYHR2lubmZ77//npqaGtfRLIWFhZw4cYLNmzfj5+cnlpWEdyaCvAyUzh3T09N0d3dz7do1rl27xtOnT/Hy8mLPnj0cP36crKwsoqKixK208N5EkD8y5VZ6dHSUmzdvUl5ezu3btxkYGCAxMZEDBw6Qn5/P9u3bCQoKemOAldltpSeXMlovHbGXvs/r/l1wXyLIH5Esy0xNTdHd3U1tbS1Xr16lubkZtVrN7t27iY+Px8fHh+bmZjo7O4mIiCA1NZXo6Gh8fX1dn8PhcNDf309zczPDw8N4e3uTkpLCxo0bCQkJQaVS4XA46O3t5eHDhwwPDxMUFERqaiopKSniOXsNEEH+CGRZxm63Mzs7y4MHD1x10qOjo/j7+5OWlkZeXh6Li4s0Nja6unrExMRw+PBhjh8/Tnx8PB4eHjidTqanp6mpqeHUqVM8efIEX19fsrKyOH78OPv27cPLy4uFhQXu37/Pn/70J54+fUp4eDjHjh0jLCzMdSC54L7ET/cDk2UZq9XK8PAw1dXVnD9/noaGBubn50lKSuLEiRPExcXx+9//nvDwcP7+7/+e0NBQ+vv7OXXqFBcuXMBkMhEUFITRaGR6epobN25w69Yt0tPT+d3vfsfs7Cz//u//zp///GfCw8OJiYnh6dOnTE5OcvDgQTZt2sTAwABms5mbN2+Sk5NDcHDwSn9rhI9IBPkDcjgczM3N0dbWRnl5OdXV1XR1dQGQn5/PoUOH2LdvH35+flitVgwGA9u2bcNgMBAbG0tdXR0dHR0sLCy4tjCOjY1RXV2Np6cn2dnZ7Nq1C5vNxrVr1xgbG6OpqYmQkBDm5+dxOByEhISQlJSEw+FgfHyc+fl5JEla4e+M8LGJIH8AygTT0NAQjY2NlJWVUVlZyYsXL4iPjycnJ4fjx4+zdetWgoKCADh58qTrY+fm5hgcHESr1bJ582YSEhLQ6XTIssz4+DiNjY3k5uaSkpKCr68vOp2OjIwM7t69S09PD4uLi4SEhODl5UVbWxujo6NMTU3h5+dHbGwsPj4+K/ntEZaBCPIvJEkSMzMzDA4OUlZWxqVLl3j8+DEeHh5kZmZy5MgRvvzySwIDA9Fqta5JJ0mSmJycZGhoiPb2dm7duoVKpeLEiRNkZGSg1WpxOBxYrVZGRkbQaDT4+/ujVquRJIng4GC8vLwYHx/H4XAQFRVFZGQkDQ0N3L17F5PJRFFREZs2bXJNnAnuSwT5Z1JKLOfm5qivr+dPf/oTt2/fZnR0FD8/P4qLi/n888/ZsWMHgYGBr3TukGWZW7du8e2339LW1oZarebgwYPExcWh0+lc76/cYi9dUgLw9PTEbDZjtVqxWq14e3uza9cuNm7cyOzsLFqtlsDAQPz8/MQmizVABPlnUCq0lPY7169fp76+HrvdTnp6OsXFxezbt4+0tDRXccePl39UKhVxcXEcPXqUzMxMBgcHGRwc5PTp0/zt3/4tSUlJL60Zv+4aJEnCbrcjyzJqtRqDwUBAQACSJKFSqUTbnzVEBPk9KGu64+PjtLa2Ul5eTlVVFSMjI4SEhLBlyxby8vLIz8/HZDLh7e39xiCp1Wo2btxIQkICi4uLPHr0iP/8z//k7t27ZGZmsn79etez7Y9HY4Ver8fX19e1K0opJhEj8NojgvyOlFF4aGiIe/fucfr0ae7evYvZbCY6OtrVfic5ORl/f/93WrfVaDRoNBq8vb1JTU1l165dTE1N8ezZM6anp11/CDw8PHA4HDgcDtcobbfb8fPzQ6/X4+3t/bG/fOETJ4L8DpROlo8fP+bSpUtcvHiRgYEBvL29iYyMxGQyERsbS2RkJP7+/j85Itrtdtftr4eHB2q1Gg8PDzQaDV5eXq6e1CqVCm9vb4xGI5OTk7x48QKj0YhKpWJ4eJjFxUXi4+Px8vJapu+E8KkSQX4LSZJcG/9v3bpFWVkZ1dXVDAwMEBsby6FDh1i3bh0DAwP09/djsVgIDw9/6+dUlpS++eYboqKiOHDgAHq9nsnJSTo6OhgZGWH9+vWuGWqDwcDmzZt59uwZ7e3tREZGYrPZXIeWJycni1lpQQT5bRYXF109tM6ePUt9fT0A27Zt4/Dhwxw9epTg4GAqKys5f/48bW1txMXFodfr3zrJND8/T1NTE01NTUxMTBAYGIjZbGZwcJD4+HgSExPx8/NDlmVCQkLIz8/n0qVL1NbWMjc3x/z8PDMzM6Snp7u2PAprmwjyEspyj91ux2w209XVRVlZGeXl5Tx//hyj0ehaG87OznZt/N+0aRP37t2jvb2dsLAw9u3b99ZtiIGBgfzmN7+hpqaGqqoqFhYW0Ol0bNu2jf379xMREeH6Q+Dv7092djbz8/PU1NRw5swZVy+v/Px8wsLCRB21IIK81NJTDisqKqisrKS+vp6JiQkiIyM5ceIERUVFbNy48aVnYZPJxN69e7l48SJVVVVkZ2e/cceRSqVCr9eTlZVFZGQkIyMjLC4uotVqCQ8Pf2m2WqVSodFoWL9+PcXFxaSlpTE1NYVGoyE2NpbQ0FDxfCwAIsguygFpjY2NVFRUUFtbS19fH35+fpSWlrJv3z727t1LdHT0K8tKBoOBzMxM6uvrGRkZoaenx1XY8TpqtRpfX18SEhKIi4tDkiTUarVr0mvp51YmxNatW0dwcLBrKUqZJBNWlrKKoFipdXsRZP4arMXFRRoaGmhoaKCsrIz5+Xmio6Ndx5RmZmbi6+v72iILT09P1q1bR1xcHDMzM3R2dhIcHPzGICuv+a5BVIIr1oc/Pco2U1mWXROUK1GIs+aDrHTwmJub48yZM6hUKry8vNi2bRtffvklBw8exGQy4eXl9daOG8rElF6v5/nz58zNzS3zVyIsN+Ws6t7eXqamplx3YXq9Hq1Wu6zXsuaDrBwabrVasdvtREVFkZubS1FREVu2bHGdNfy2v7BLb38DAgJ4/vw58/Pzy/hVCCtBWeePiori4cOH/Nd//RcGg4EdO3aQmpqKVqvFx8dnWUboNR1k5XlTKcJIT0/nxIkT5Ofnk5iY6HoWXtor601UKhUREREYjUaePn3KwsKC2Ae8Bnh4eBAYGEh8fDw9PT3U1dXR1tZGUlISW7duJTs7G19fXxHkj0mlUuHj40NoaChqtRpPT0/m5uZobm6mubn5J8O79PPIsszMzAz379+nubmZixcv0tnZ6dq5JLi/xcVFBgcHaWtro7Kyki1btvD48WP27NnDhg0b0Ov1H+2113SQ4a+TTnq9nsDAQO7fv09PT89Lk0rvEsKlo7bT6cTpdPLNN9+4NjOIILuvpSOt0vLYZrMhSRI3b96ktbUVi8XCb3/7W1ev8o9yHfIa/y1Tlp26urqwWCzvdBv9OsoPSHkecjqdIsBrwNKf++TkJL///e958OABWq2W3bt3k5eXR1ZWFnFxcR91AmzNB1kJrlJXLQjvQ/n9efHiBTU1Ndy9exdZlklMTCQjI4P09HRX8dDHXPdf87fWypKSKK4Qfg6l1VN3dzfd3d2kpqa6Zq29vb1fKfD5WNb8iCwIv4TD4WBwcJAXL14QGhrq2iOu3EYvV2GICLIg/AKSJLlaDr+p8m85iCALwi+0NEKi1lpYE5S1VrvdjsFgYN26db+4hlxZwx8dHWVubg6TyURoaOjy3dZ+Ag0ORZCFZTU9Pc3Zs2exWCzs2rWLoqKiX7wsI8sy/f39lJeXM+rhYrIAAAYpSURBVDAwwGeffUZwcPCa2mQipmqFZaWMnpOTkywuLn6w0WxmZgaLxYK/v/9HLbz4VIkRWfiglla4LT2rWdne5+Pjw/79+5mfnycqKgqVSuVq9v/jBv5L92m/aRJJ+djw8HD279+PTqdzfd7l+Do/lTOoRZCFD0opUxweHmZiYgKHw4GPj4/rhMnZ2VkCAgJYt26dq8Z9enqaoaEh7HY7RqMRDw8PJicnGR8fR6/XExER8cajYW02Gz09PVgsFoKCglw90z4mpR3U3Nwc3t7eLx0FtFJEkIUPanx8nOrqaleHFZvNhlqtpqioiMOHD9PT08MPP/yAr68vR44cITc3l2fPnvH999/T2dlJRkYGUVFRPHr0iDt37hAUFMQXX3xBQUEBBoPhlcIdm83GxYsXOX/+POHh4fzLv/wLaWlpHz1Yi4uLdHV14enpicFgIDAwEL1ev2wFID8mnpGFD0aSJPr6+jh9+jTT09OUlpby+eefYzKZmJiYwGazER4ejslkQpIkzGYzTqeTwMBAYmNjsdlsVFdXYzab2bJlC9nZ2VgsFurr6+nr63ttCa2HhwfJycmsX78ei8Xyk3vHPxQvLy/8/f25ffs23377LXV1dVgslpcOEVhOYkQWPqiFhQUGBwdJTEwkMzOTmJgYMjIycDgchIWFoVKp2Lx5M729va7n3oCAAFJSUuju7mZwcJCNGze6js0ZGhpibm7O1U5HeS5VqNVqTCYTqampmM1mDAbDK0FWgqVsKf0QQVOr1axfv560tDSuX7/O+fPnuXHjBtu3b3fdVXh5eS3bzLkIsvDBqNVqAgMD2bRpEzabjaamJgBiY2PR6/X4+PgwMzODl5cXGo3mpZ1Dnp6eBAUFERAQ4Nq76+/vj9FofOtOMqXrqdPpJDY29o3nbS0sLDA6Osr4+DhWq/UXf63KBJ7SlKKuro6xsTHu3btHYWEhe/bsITk5maCgoGVpVyyCLHxQ8fHx/O53v6OiooJLly7x3XffsX//fo4cOUJKSsobP06WZTw8PF46Lkd5+9tmhp1Op2tS7U0TYsrupB9++IGKigqGh4c/yLOssl11bm6OiYkJrFYrDQ0NdHZ2cvPmTX7729+Sl5eHv7+/6BAirB6yLLt6bh8+fJjo6Giam5tpbW1Fr9e7loWURgw/pvzb+/zS2+12+vr6mJubIzIy8rV9vlUqFUajkX379hEVFcXMzMwvXjZSrn9hYYGOjg7q6+sZGBjAaDSybds2CgoKSEpKcvUo/9hEkIUPQjmtcnh4mMHBQRISEigpKSE6Opp//dd/5dGjR64lIuV9rVbrS4G22+0v3UYrt6/KGdCvvCawYLXS19fnauSvdGVZSglydnY22dnZH+zrXVxcpLm5mYmJCTZs2EB6ejopKSns2rWLrVu3us7GXg4iyMIHY7PZ6O7u5uzZs0RGRpKamsqLFy/w9vZm/fr1eHl5MTMzw+PHj2loaGBiYoLdu3djNBrp6+vjwYMHOBwOduzYgU6nY3h4mP7+fiYnJ8nIyGDr1q0vnasl2e1I8/Pk7ttHVHQ0kZGRy/I8qux4GhgYoKOjA6vVSnZ2Nnl5eYSFhbm2MS7nMpQIsvDBKE30zWYzVVVVSJKETqdjx44d7Nmzh+DgYNrb22loaODBgwdMTU3x8OFDEhIS6OjooLGxEYfDwYMHDwBob2+nv7+foaEhmpubycvLc20VRJaRFhYI1Ov54osv8Pz/s6aXIzxOpxOLxUJ3dzfR0dFkZ2djMplch86LbYzCquZ0OjGbzXR3d/PixQusViteXl7ExMQQHx+Pv78/ExMTtLS0uOqiN27ciF6vZ2hoiKdPnwKwYcMGjEYjU1NT9Pb2Mjs7S2xsLCkpKS/drkrj46gCApCXPlsrv84fMUxKn7eJiQlXQ3olwCtV4SWCLHxQTqfT1f9saZ21Mkus1EYvPcMKXl7jVd5XqbdW3vbjY3bk2VlUOh0sfQ6VZXA44DXPyh/S0vXoT6FNlAiysGrJ8/Og0aD6yKFdDcQzsrBqqby9V/oSPhliRBYEN7DyN/eCIPxiIsiC4AZEkAXBDYggC4IbEEEWBDcggiwIbkAEWRDcgAiyILiB/wMn+CMp9RFz+wAAAABJRU5ErkJggg==)
physics-General