Q. 93.7( 3 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 ∞-∞,1 .. etc.)


Let Z =


As it is taking indeterminate form-


we need to take steps to remove this form so that we can get a finite value.


Z =


Take the log to bring the power term in the product so that we can solve it more easily.


Taking log both sides-


log Z =


{ log am = m log a}


Now it gives us a form that can be reduced to


log Z =


Dividing numerator and denominator by to get the desired form and using algebra of limits we have-


log Z =


if we assume then as xa y 0


log Z =


Use the formula-


log Z =


log Z =


Now it gives us a form that can be reduced to


Try to use it. We are basically proceeding with a hit and trial attempt.


log Z =


sin (A+B) = sin A cos B + cos A sin B


log Z =


log Z=


log Z =


log Z =


Use the formula-


log Z = cot a – 0


log Z = cot a


Z = ecot a


Hence,



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