# 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

It also involves a trigonometric term, so there is a possibility of application of Sandwich theorem-

As Z =

Adding and subtracting 1 in the numerator to get the desired form

Z =

Z =

{using algebra of limits}

To get the desired form to apply the formula we need to divide numerator and denominator by x.

Z

Using algebra of limits, we have-

Z

Use the formula: and

Z =

{ log e = 1}

Z = 1/2

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
RELATED QUESTIONS :

Evaluate the following limits:

RD Sharma - Mathematics

Evaluate the following limits:

RD Sharma - Mathematics

Evaluate the following limits:

RD Sharma - Mathematics

Evaluate the following limits:

RD Sharma - Mathematics

Evaluate the following limits:

RD Sharma - Mathematics

Evaluate the following limits:

RD Sharma - Mathematics

Evaluate the following limits:

RD Sharma - Mathematics

Evaluate

RS Aggarwal - Mathematics

Evaluate

RS Aggarwal - Mathematics

Evaluate

RS Aggarwal - Mathematics