Q. 29

# 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 = To apply the formula we need to get the form as present in the formula. So we proceed as follows-

Z = Multiplying numerator and denominator by √(1+cos x)

Z = Using (a+b)(a-b) = a2-b2

Z = √(1-cos2x) = sin x

Z = {using algebra of limits}

Z = Dividing numerator and denominator by x-

Z = Z = Use the formula: and Z = { log e = 1}

Hence, Rate this question :

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