How to prove <munder> <mo form="prefix">lim <mrow class="MJX-TeXAtom-ORD"> x

Mackenzie Rios

Mackenzie Rios

Answered question

2022-05-28

How to prove lim x 0 tan ( x ) x = 1?

Answer & Explanation

Bruce Bridges

Bruce Bridges

Beginner2022-05-29Added 13 answers

lim x 0 tan x x = lim x 0 sin x x lim x 0 1 cos x = 1 × 1 = 1
since the two limits exist.
Emely Baldwin

Emely Baldwin

Beginner2022-05-30Added 1 answers

If you know the proof of lim x 0 sin x / x = 1 then you may know about following inequality,
cos ( x ) sin ( x ) x 1
Dividing by cos x,
1 tan ( x ) x sec x
Taking the limit,
1 lim x 0 tan ( x ) x 1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?