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,