Prove \lim_(x \to 0) (sin x)/(x) = 1

Question

Prove
`\lim_(x \to 0) (sin x)/(x) = 1`

Answer 1

See below.

Explanation:

sin x / x.

You can prove this by L'Hopitals Rule.

If x = 0 then the function = 0/0 so the above rule is applicable here.

Differentiating top and bottom we get cos x / 1 = cos x.

Limit x --> 0 of cos x = 1 so it is proved.