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 = (indeterminate form)

∴ 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

Note: While modifying be careful that you don’t introduce any zero terms in the denominator

As Z

Multiplying both numerator and denominator by √(4+x)+2 so that we can remove the indeterminate form.

∴ Z

⇒ Z

{using a² - b² = (a + b)(a - b)}

⇒ Z

Using basic algebra of limits-

Z =

⇒ Z = 4

Use the formula:

∴ Z = 4log 5

Or,