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 and also use of sandwich theorem -

To get the desired forms, we need to include mx and nx as follows:

As Z

⇒ Z {Adding and subtracting 1 in numerator}

⇒ Z

{using algebra of limits}

To get the form as present in the formula we multiply and divide x into both terms respectively:

∴ Z

{manipulating to get the forms present in formulae}

Z

Use the formula: and

∴ Z

Hence,