Q. 385.0( 1 Vote )

# 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 limits.

Z =

To get the desired form, we proceed as follows-

Dividing numerator and denominator by tan x-

Z =

Using algebra of limits-

Z =

Use the formula - (sandwich theorem)

Z =

As, x 0

tan x 0

Let, y = tan x

if x 0 y0

Hence, Z can be rewritten as-

Use the formula:

Z = log e = 1

{ log e = 1}

Hence,

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