Why does the limit as x goes to 0 of cos &#x2061;<!-- ⁡ --> 1 x

Winigefx

Winigefx

Answered question

2022-06-12

Why does the limit as x goes to 0 of cos 1 x not exist?
Use two different sequences: x n = 1 n π , and y n = 2 ( 2 n + 1 ) π and show that lim cos 1 x n lim cos 1 y n

Answer & Explanation

scoseBexgofvc

scoseBexgofvc

Beginner2022-06-13Added 20 answers

lim x 0 cos 1 x = cos ( 1 0 ) = cos ( )
Between -1 to 1 ( | cos 0 | 1)
Thus, limit doesn’t exist

Given, x n = 1 n π
y n = 2 ( 2 n + 1 ) π

lim x n 1 n π cos ( 1 x n ) = cos ( 1 1 n π )
= cos ( n π )
= { 1 ;   i f   n   i s   e v e n 1 ;   i f   n   i s   o d d

lim y n 2 ( 2 n + 1 ) π cos ( 1 y n ) = cos ( 1 2 ( 2 n + 1 ) π )
= cos ( 2 n + 1 ) π 2
= 0
Thus, lim cos ( 1 x n ) lim cos ( 1 y n )
juanberrio8a

juanberrio8a

Beginner2022-06-14Added 7 answers

Thanks for fast answer

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