Show analytically that 0 is the only zero of sin ⁡ ( 2 x )...

delirija7z

delirija7z

Answered

2022-07-10

Show analytically that 0 is the only zero of sin ( 2 x ) + 2 x
I tried:
0 = sin ( 2 x ) + 2 x 0 = 2 sin x cos x + 2 x 0 = 2 ( sin x cos x + x ) 0 = sin x 1 sin 2 x + x 0 = sin 2 x ( 1 sin 2 x ) + x 0 = sin 2 x sin 4 x + x ? ? ?

Answer & Explanation

persstemc1

persstemc1

Expert

2022-07-11Added 18 answers

Hint: Consider the increasing/decreasing behavior of the function f ( x ) = sin ( 2 x ) + 2 x
f ( x ) = 2 cos ( 2 x ) + 2. Since the range of cos θ is [ 1 , 1 ], we know that 2 cos ( 2 x ) + 2 0, so f is (non-strictly) increasing for all real numbers.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

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

Didn't find what you were looking for?