Q. 215.0( 3 Votes )

Evaluate <i

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


It also involves a trigonometric term, so there is a possibility of application of Sandwich theorem-


As Z =


Adding and subtracting 1 in the numerator to get the desired form


Z =


Z =


{using algebra of limits}


To get the desired form to apply the formula we need to divide numerator and denominator by x.


Z


Using algebra of limits, we have-


Z


Use the formula: and


Z =


{ log e = 1}


Z = 1/2


Hence,


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