Question

Lim┬(x→0) 〖sin〗^2 /(3x^2 )

lim┬(x→0) sin x / 5 √x

Answer 1

1) lim x->0  sin²x/3x²
= lim x->0 sin(x)/x * sin(x)/x * 1/3
= 1 * 1 * 1/3
= 1/3

2) lim x->0  sin(x)/5√x
= lim x->0 sin(x)/5√x  * √x/√x
= lim x->0  √x/5 * sin(x)/x
= √0 / 5  * 1
= 0 * 1
= 0