Q. 64.3( 4 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


As Z


Z


{using (a-b)2 = a2+b2-2ab}


Z


To apply the formula we need to bring the exact form present in the formula, so-


Z


{Adding and subtracting 1 in numerator}


Z


Using algebra of limits-


Z


Use the formula:


Z =


Hence,



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