Q. 63.5( 4 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 term in the product so that we can solve it more easily.


Taking log both sides-


log Z =


log Z =


{ log am = m log a}


log Z =


{using algebra of limits}


Still, if we put x = ∞ we get an indeterminate form,


Take the highest power of x common and try to bring x in the denominator of a term so that if we put x = ∞ term reduces to 0.


log Z =


log Z =


log Z =


log Z =


Loge Z =


Z = 1/2


Hence,



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