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,