Question

`\binom{lim}{x -> 0} ( \sin^(2) (x) )/(x)`

I looked up how to do this, but I just dont understand how the internet explains it, I need a step by step simple explanation on how to do it.​

Answer 1

0

Explanation:

To solve this without L'Hopital's rule, you need to use this identity:

lim(x→0) (sin x / x) = 1

lim(x→0) (sin²x / x)

lim(x→0) (sin x / x) (sin x)

lim(x→0) (sin x / x) · lim(x→0) (sin x)

1 · 0

0

Alternatively, since plugging in x=0 gets 0/0, we can use L'Hopital's rule. Replace the numerator and denominator with their derivatives.

lim(x→0) (sin²x / x)

lim(x→0) (2 sin x cos x / 1)

0