Question

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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:

We first try substitution:

=

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.

( )

On substituting, We get

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or

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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