Question

How do you evaluate the limit `(cos(2x)-1)/(2x^2)` as x approaches `0`?

Answer 1

`-1`.

Explanation:

Utilising the Identity : `(1-cos2theta)=2sin^2theta`, we have,

`"The Limit"=lim_(x to 0)(cos2x-1)/(2x^2)`,

`=lim_(x to 0)(-2sin^2x)/(2x^2)`,

`=lim_(x to 0)-(sinx/x)^2`,

`=-(1)^2`,

`=-1`.