Evaluate .

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,