Question
- 4
![2 square root of 2](data:image/png;base64,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)
![fraction numerator 1 over denominator square root of 2 end fraction](data:image/png;base64,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)
![square root of 2](data:image/png;base64,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)
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: 4
![Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x over denominator square root of x plus 4 end root minus 2 end fraction](data:image/png;base64,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)
We first try substitution:
![Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x over denominator square root of x plus 4 end root minus 2 end fraction equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ0AAAAnCAYAAAAVd0rFAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAU2v5G4wAAAzBJREFUeNrtnD9oFEEUxocgh4QrFBULDZEQgoikMmhQESGIyFWSwmAlWoiIXGlhIaTQSkFtRCGFYED8hwQVJIgEkYioWIgowVIkoJBCJajn99x3eCx3udmdmd077/vBR/Zuye7y7tv3ZmZnxxiSNYehs3W+H9d9hAThJbS25vMh6BLDQkKyFzqn2yPQNENCsuARtAt6Da1iOEgWlKFFaJChIFmwHbqpJXaM4SCh6YPuQd1QEXrB8kpCsga6HzNZCbrWqQGp0BNBKUC3oXV19k1qj5ami/GFviFZm46ZkGRqukpMhDDTkVx900w0HWGmy+vuo5KJpiMsr6GRAdR3qhJ/584pr/JwuiuH6xqGnphoFF/0WL8jHWA6mYLT6OH0jPk3W0KM+RDqtTzvhImeQTbirommAFXZaaJnl+Q/r83CbuhzA3NKyZvUbZk5sT/Bea9A76GtDfYvxDJsl35HyN9MWFYT1eNYE2P/hAYsM/Ci52svsifZnlzQhn4h4f+JSeegIctMtyxApjugbUXSRoxoeX1rouk7SUjappPtKc/X/wA6wp+xfejR3mVRS+h4gN6rZKGVamg51z6Px18NfdW/pA0oaM91oObzXJPMlYaSdjZketUJz8c+Ct1pwdiWMmi/VafNL2g7WdrlB2nr8EgWHW2xaypqUyW06aRqjNUkiU3QU8P3NoKyAZqHlgc8RxrjXDbR2/559FRlfPUNrRGOk6bxEI8xfpaASGocKXnTDob1wQ9aIxyvTPN3E1yXgEhinIJmmd4cTTesJZZ4aCPF2Qx9MtG431K4LgGRxDiSVY87lmYXpJkxq9mWpKTfROOA8uPtiO07A523PE6SJSDSPlEYrJNhKgmM7foUQ4akZEx0D23jxik1nYzDPY/t+whtsTyOyxIQtsaZ1ZvEtROShj41XD8t4w8ZtP5d0zbbBn2wKK3Vhr3LEhC+slUoNmpnqps28c836LpuX4ROW2YA1yUgXAwTOtPJTXjD8uYjKbgKfdcAz+sdvhS+loBoZdNNWcSBOLAC+gXdgp5ZDF20whIQlQyOz+lTgZnRgJYZCpIVQ2q69QwFyZJRhiBf/gAHdmewOFmP/AAAASF0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+THQ8L21pPjxtcm93PjxtaT54PC9taT48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3gyMTkyOzwvbW8+PG1uPjA8L21uPjwvbXJvdz48L21zdWI+PG1vPiYjeEEwOzwvbW8+PG1mcmFjPjxtaT54PC9taT48bXJvdz48bXNxcnQ+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+NDwvbW4+PC9tc3FydD48bW8+JiN4MjIxMjs8L21vPjxtbj4yPC9tbj48L21yb3c+PC9tZnJhYz48bW8+PTwvbW8+PC9tYXRoPmsAds4AAAAASUVORK5CYII=)
![Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator 0 over denominator square root of 0 plus 4 end root minus 2 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.
![Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x over denominator square root of x plus 4 end root minus 2 end fraction](data:image/png;base64,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)
![Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator begin display style fraction numerator d over denominator d x end fraction end style x over denominator fraction numerator d over denominator d x end fraction square root of x plus 4 end root minus 0 end fraction space space space space space space left parenthesis space A p p l y space L apostrophe H o p i t a l apostrophe s space r u l e right parenthesis
Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator begin display style 1 end style over denominator begin display style fraction numerator 1 over denominator 2 square root of x plus 4 end root end fraction end style end fraction space equals Lt subscript x not stretchy rightwards arrow 0 end subscript space 2 square root of x plus 4 end root space
p u t space x equals 0 space t h e n comma
space 2 square root of x plus 4 end root space equals space 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We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
Related Questions to study
The excess of pressure inside a soap bubble than that of the other pressure is
The excess of pressure inside a soap bubble than that of the other pressure is
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
Two wires of same diameter of the same material having the length
and 2
If the force is applied on each, what will be the ratio of the work done in the two wires?
Two wires of same diameter of the same material having the length
and 2
If the force is applied on each, what will be the ratio of the work done in the two wires?
A graph is shown between stress and strain for metals. The part in which Hooke's law holds good is
![](data:image/png;base64,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)
A graph is shown between stress and strain for metals. The part in which Hooke's law holds good is
![](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 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
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means