# 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.

As, Z = Z = Taking log both sides-

log Z = log Z = { log am = m log a}

Now it gives us a form that can be reduced to Adding and subtracting 1 to cos x to get the form-

log Z = Dividing numerator and denominator by cos x + a sin x– 1 to match with form in formula

log Z = using algebra of limits –

log Z = A = Let, cos x + asin x - 1 = y

As x0 y0

A = Use the formula - A = 1

Now, B = cos x – 1 = -2sin2(x/2) and sin x = 2sin(x/2)cos(x/2)

B = B = B = Use the formula - B = B = 1/a

Hence,

log Z = loge Z = a

Z = ea = ea

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 