Answer :

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 =

Adding and subtracting 1 in the numerator to get the desired form

⇒ Z =

⇒ Z =

{using algebra of limits}

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

⇒ Z

Using algebra of limits, we have-

Z

Use the formula: and

∴ Z =

{∵ log e = 1}

⇒ Z = 1/2

Hence,

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