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, Rate this question :

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