Question

Limit as x approaches 0 of (sin^2x)/x

Answer 1

0

Explanation:

Given the expression

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

Substitute the value of x in the function

`= (sin ^2(0))/(0)\\= 0/0 (indeterminate) \\`

Apply l'hospital rule

`\lim_(x \to \ 0) (d/dx(sin^2x))/(d/dx(x)) \\= \lim_(x \to \ 0) ((2sinxcosx))/(1) \\`

Substitute the value of x

= 2 sin(0)cos(0)

= 2 * 0 * 1

= 0

Hence the limit of the function is 0