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

∴ 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.

Use the formula: and

As Z =

To get the above forms, we need to divide numerator and denominator by x.

∴ Z {using basic limit algebra}

⇒ Z {using the formulae described above}

Hence,