Q. 305.0( 2 Votes )

Evaluate the following limits:


Answer :

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 limits.


As Z =


Z =


Z =


{using properties of exponents}


Z =


{using algebra of limits}


As, x 5


x-5 0


Let, y = x-5


if x5 y0


Hence, Z can be rewritten as-


Z =


Use the formula:


Z = e5 log e


{ log e = 1}


Hence,



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