Q. 375.0( 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 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.

As Z = Z = Z = {using properties of exponents}

Z = {using algebra of limits}

Z = Z = As, x 0

bx-sin x 0

Let, y = bx-sin x

if x0 y0

Hence, Z can be rewritten as-

Z = Use the formula: Z = log e =1

{ log e = 1}

Hence, Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 