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
This question is a direct application of limits formula of exponential and logarithmic limits.
As Z =
⇒ Z =
{Adding and subtracting 1 in numerator}
⇒ Z =
{using algebra of limits}
To get the form as present in the formula we multiply and divide 3 and 2 into both terms respectively:
⇒ Z =
Use the formula:
∴ Z = 3log e – 2log e= 3-2 = 1
{using log e = 1}
Hence,