Evaluate the following limits:

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 a formula, we move as follows-


As Z =


Z =


Using algebra of limits we have-


Z =


Use the formula:



Hence,



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