Q. 435.0( 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 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 algebra of limits}


Z =


Z = { sin(x-π/2) = -cos x}


As xπ/2


x-π/20


Let x-π/2 = y and y0


Z can be rewritten as-


Z =


Dividing numerator and denominator by sin y to get the form present in the formula


Z =


Using algebra of limits:


Z =


Use the formula: and


Z =


Hence,



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