Question

How do you evaluate the limit `(sin^2x)/(xcosx)` as x approaches `0`?

Answer 1

0

Explanation:

`lim_(x to 0) (sin^2x)/(xcosx)`

`lim_(z to 0) (sin z)/z = 1` is a well known limit so we aim to find that in the mix

`= lim_(x to 0) (sin x)/x* tan x`

we know each of these limits so the limit of the product is the product of the limits
`= lim_(x to 0) (sin x)/x * lim_(x to 0) tan x`

`= 1 * 0 = 0`