# 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 ∞-∞,1 .. etc.)

Let Z =

As it is taking indeterminate form-

we need to take steps to remove this form so that we can get a finite value.

Z =

Take the log to bring the power term in the product so that we can solve it more easily.

Taking log both sides-

log Z =

{ log am = m log a}

Now it gives us a form that can be reduced to

log Z =

Dividing numerator and denominator by to get the desired form and using algebra of limits we have-

log Z =

if we assume then as xa y 0

log Z =

Use the formula-

log Z =

log Z =

Now it gives us a form that can be reduced to

Try to use it. We are basically proceeding with a hit and trial attempt.

log Z =

sin (A+B) = sin A cos B + cos A sin B

log Z =

log Z=

log Z =

log Z =

Use the formula-

log Z = cot a – 0

log Z = cot a

Z = ecot a

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