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,
![]()