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 =


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


Using algebra of limit, we can write that


Z =


Use the formula:


Z =


Hence,



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