Q. 12

Evaluate the following limits:


Answer :

As we need to find


We can directly find the limiting value of a function by putting the value of the variable at which the limiting value is asked if it does not take any indeterminate form (0/0 or ∞/∞ or ∞-∞, .. etc.)


Let Z


We need to take steps to remove this form so that we can get a finite value.


TIP: Most of the problems of logarithmic and exponential limits are solved using the formula and


This question is a direct application of limits formula of exponential and logarithmic limits.


To get similar forms as in formula, we move as follows-


Let 1/x = y


As x y 0


Z can be rewritten as-


Z


Use the formula:


Z =


Hence,



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