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 of logarithmic limits we need to get the form that matches with one in formula

∴ dividing numerator and denominator by x³

⇒ Z =

⇒ Z =

⇒ Z =

{using algebra of limits}

Use the formula: and

∴ Z = 1/1

Hence,