Q. 215.0( 1 Vote )

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 =


To apply the formula of logarithmic limits we need to get the form that matches with one in formula


We proceed as follows-


Z =


{using properties of log}


Z =


To apply the formula of logarithmic limit, we need the x/2 denominator


multiplying 1/2 in numerator and denominator


Hence, Z can be rewritten as-


Z =


Z =


{Using algebra of limits}


As x0


Let,


Z =


Use the formula:


Z =


Hence,



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