Compute lim x → 0 sin 3 ⁡ x ( 2 x ) 3

aggierabz2006zw

aggierabz2006zw

Answered

2022-07-09

Compute lim x 0 sin 3 x ( 2 x ) 3

Answer & Explanation

Wade Atkinson

Wade Atkinson

Expert

2022-07-10Added 12 answers

depending on the fact of lim x 0 sin x x = 1
sin 3 8 x 3 = 1 8 sin x x sin x x sin x x
ziphumulegn

ziphumulegn

Expert

2022-07-11Added 4 answers

Recall that if f is continuous, then
lim x a f ( g ( x ) ) = f ( lim x a g ( x ) ) .
Since the cube function x x 3 is continuous, we have
lim x 0 sin 3 x ( 2 x ) 3 = ( 1 2 lim x 0 sin x x ) 3 = ( 1 2 ) 3 = 1 8 .

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