How do you find the limit of (1-cos x)/x as x approaches 0?

Guadalupe Cooke

Guadalupe Cooke

Answered question

2023-02-17

How to find the limit of 1 - cos x x as x approaches 0?

Answer & Explanation

Prince Mora

Prince Mora

Beginner2023-02-18Added 2 answers

1 - cos x = 2 sin 2 ( x 2 ) so
1 - cos x x = ( x 4 ) ( sin ( x 2 ) x 2 ) 2 then
lim x 0 1 - cos x x lim x 0 ( x 4 ) ( sin ( x 2 ) x 2 ) 2 = 0 1 = 0
Hence, 0.
Rory Moran

Rory Moran

Beginner2023-02-19Added 1 answers

Multiply by 1 + cos x 1 + cos x for get
1 - cos 2 x x ( 1 + cos x ) = sin 2 x x ( 1 + cos x )
= sin x sin x x 1 1 + cos x
Taking the limit as x 0 gives
( 0 ) ( 1 ) ( 1 2 ) = 0

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