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

As Z =

∴ Z = {using (a+b)² = a²+b²+2ab}

Using algebra of limit, we can write that

Z =

Use the formula:

∴ Z =

Hence,