Q. 375.0( 1 Vote )

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 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


This question is a direct application of limits formula of exponential limits.


As Z =


Z =


Z =


{using properties of exponents}


Z =


{using algebra of limits}


Z =


Z =


As, x 0


bx-sin x 0


Let, y = bx-sin x


if x0 y0


Hence, Z can be rewritten as-


Z =


Use the formula:


Z = log e =1


{ log e = 1}


Hence,



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