Whether exits or not.
The function .
Suppose an inequality of functions in a interval around c and that . Then .
A function is differentiable at point x, then .
Consider the function when and ,
By definition, .
Substitute in the above equation,
Since the value of lies between to 1.
That is .
Multiply throughout by h,
Thus and .
By squeeze theorem,
Therefore, the limit of exist.
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