Evaluate the following limits:

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.


Note: While modifying be careful that you don’t introduce any zero terms in the denominator


As





Z =


{Using basic limits algebra}



(1- 2sin2x) = cos 2x




As, a2 – b2 = (a+b)(a-b)


Z =


Now put the value of x, we have-


Z =


Hence,



2