Question
If 
, then the value of 
is
- -5
- 5
none of these
none of these
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: 5
If , then the value of
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.
= 
{ apply L'Hopital's rule }
,
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
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as shown in figure. Find the distance of centre of mass of the system from geometrical center of square.
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If 
then 
has the value
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If 
then 
is
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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.
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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.
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.
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.
