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


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


Z


Z


xa x/a 1


x/a – 1 0


Let, (x/a)-1 = y


y0


Hence, Z can be rewritten as-


Z


Use the formula:


Z


Hence,



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