# 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 get rid of indeterminate form we will divide numerator and denominator by sin x

Z

Using Algebra of limits we have-

Z

Where, A

and B

{from sandwich theorem}

As A

Let, sin x =y

As x0 y0

A

Using

A = log e = 1

Hence,

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