Q. 42

# 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 = As, 1-cos x = 2sin2(x/2)

Z = Z = To get the desired form to apply the formula we need to divide numerator and denominator by x2.

Z = Using algebra of limits, we have-

Z = Use the formula: and Z = Z = 2 log e = 2

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