Q. 13

# 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 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, Rate this question :

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