Question
Hint:
In this question, we have to find limt value of
.
The correct answer is: ![11 over 13](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 x cubed minus 3 x plus 4 over denominator 13 x cubed minus 5 x squared minus 7 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKoAAAAqCAYAAAAjxsBaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAABElJREFUeNrtXU1IVUEUHh4iESKEiEhEICISIUFIhEQEIhEuRHhICxEJQiRC3IaLEKFVREQQES0kBIkWIhJEiESLQCRaRAQSLd20aBEPCewc7ifdXtd37/jmzJ37PB984P15752Z+e6Zn3vmaIzCF/bAXeJH4pBWiSJ09BK/azUoQkeJ+EOrQREy2oiPiJNaFYo09BDnMFZ0cZ/tOHVcqFxXiGvEX8QK8SvxAR6OkDCMelCkYJF4M0NlZb3PBq3EBXyva6wTR4nNsXPniK8DqvsW4mcVqr2Hc3mfDSoey/kz5/qL4wnxhgrVv1C50u8lnJ/HtSRcIm56KmMX8Ysju+sV6gDxreDDr0JNub5F7IgdT2LClDQ+raArPi1ctg7YwePUa3XY7UqoPBz5FCu3CjUHoV4l3sffgzGvkVeZ4pwRtNtGbOy9bwkPp1SoGe55Q7yMFYI2x2JLYhpOEEeIH2CXC7sPa1cf8b2Hcb8KNcM97Ll20SghoQVilbA7a/3x73erUPMXKk8SXqIbvR5gOStCdtvUXz29gwrVwX08q14hHof32jRhLbD3YUIlYfeeh7pXOBBqu4neBMUbmN+6LOZUng1imdhkongCflP1jTghZHcuQt07YgLN0v3Uuo+XW14RTyZ8bgkzat/g9dlVdPXMdQjQBGi3mFA12kdRiG5QxxSK4IWqszSFelSFQoWqUKEWaEavLC7VoyrUoyoUuQmVAxdKWk2K0IXKYWAHBS68M3+jb1jMNoHBz030rvkgzJrojcljE+3/2QeHsD0jPjTRPnnFERJqrQEtvzfeOUDQwxATgyNxRi1+96mJgiYuJFy7Y6J31z0QJP/2NAQ6XiXmtkDrs2iZUeJ2cwxpd6MJnRtjBsJLwnTKw/AbgozjdtXxXdw7X3WevfhYwHVTxMwoJbTZVqMJlT0ebyJrtvwcC3ub2J9wbarq+IyJYg543/pA7HwnPG/IjV7UWIlKI4l0EF0/79dut/xsrTFqGZ6Su3XeeLaM71+GWBfw1L8IeKJX5MwovEVlo1FEegqFaYFo5h1/P49dJ8z/+37O4/xYBi+elvFEKsOIdGYUyaj5ToxRuzzbLbIM2owZf0/seDtlFp8H0jKeSGYYkcyMIrW2ze25CrH6RLnGHOfIrWzYwGWGkUpBhNqJ3qXVc9t0wOkdU5naNazLDCNSmVFsypPV7jWTz7r0ivl3nVyFmuHJdpFhxEdmFFuPamO3z/jjKcwhFBka1meGEZfl2cUQhT3hbMr8IKSMLvvgB5j3/TepPO08kESGkXpnwWl2N2EVZA7Dld6C2M3YwKqL4pBdpWSGEUkMmdprnyHZXUZPoKhzTCeVYUQaRbC7BO+vE6g6hSqZYUQSZ020lh263SOmgd56+RKq7wwjrsCJJC7C5hImSyzS0cDtZiwZ/YcbmQb9cRQpw0j1GI+9PkeecdALx0D0F8Buxg4mrpnwB84MDKY8Ok3tAAABx3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3ViPjxtaT5MdDwvbWk+PG1yb3c+PG1pPng8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxOTI7PC9tbz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4MjIxRTs8L21pPjwvbXJvdz48L21zdWI+PG1mcmFjPjxtcm93Pjxtbj4xMTwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+MzwvbW4+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+NDwvbW4+PC9tcm93Pjxtcm93Pjxtbj4xMzwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+NTwvbW4+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPiYjeDIyMTI7PC9tbz48bW4+NzwvbW4+PC9tcm93PjwvbWZyYWM+PC9tYXRoPs6ggwIAAAAASUVORK5CYII=)
has indeterminate form
, but we can factor and reduce.
![Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 x cubed minus 3 x plus 4 over denominator 13 x cubed minus 5 x squared minus 7 end fraction space W e space c a n space w r i t e space i t space l i k e space Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 minus begin display style 3 over x squared end style plus begin display style 4 over x cubed end style over denominator 13 minus begin display style 5 over x end style minus begin display style 7 over x cubed end style end fraction](data:image/png;base64,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)
On substituting, We get
![space Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 11 minus begin display style 3 over x squared end style plus begin display style 4 over x cubed end style over denominator 13 minus begin display style 5 over x end style minus begin display style 7 over x cubed end style end fraction space equals space fraction numerator 11 minus 3 cross times 0 plus 4 cross times 0 over denominator 13 minus begin display style 5 cross times 0 minus 7 cross times 0 end style end fraction space equals 11 over 13](data:image/png;base64,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)
Infinite limits in calculus occur when the function is unbounded and tends toward infinity or negative infinity as x approaches a given value.
Related Questions to study
A wire of length 50 cm and cross - sectional area of 1 mm2 is extended by 1 mm what will be the required work?![open parentheses straight Y equals 2 cross times 10 to the power of 11 Nm to the power of negative 2 end exponent close parentheses](data:image/png;base64,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)
A wire of length 50 cm and cross - sectional area of 1 mm2 is extended by 1 mm what will be the required work?![open parentheses straight Y equals 2 cross times 10 to the power of 11 Nm to the power of negative 2 end exponent close parentheses](data:image/png;base64,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)
The work per unit volume to stretch the length by 1% of a wire with cross - section area 1 mm2 will be.....
The work per unit volume to stretch the length by 1% of a wire with cross - section area 1 mm2 will be.....
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
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
Young's modulus of the material of a wire is Y. On pulling the wire by a force F the increase in its length is x, what is the potential energy of the stretched wire?
Young's modulus of the material of a wire is Y. On pulling the wire by a force F the increase in its length is x, what is the potential energy of the stretched wire?
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