Question

How do you evaluate the limit `(1-cos2x)/(5x^2)` as x approaches `0`?

Answer 1

Recall `cos2x = 1-2sin^2x` and rewrite the quotient.

Explanation:

`lim_(xrarr0)(1-cos2x)/(5x^2) = lim_(xrarr0)(1-(1-2sin^2x))/(5x^2)`

`= lim_(xrarr0) (2sin^2x)/(5x^2)`

`= lim_(xrarr0) (2/5 sin^x/x sinx/x)`

`= 2/5(1)(1) = 2/5`