How do you find the limit of x/(sin x) as x approaches 0?

FeelryclurN9g3z

FeelryclurN9g3z

Answered question

2023-02-17

How to find the limit of x sin x as x approaches 0?

Answer & Explanation

abriladabchx

abriladabchx

Beginner2023-02-18Added 6 answers

Answer is 1.
Explanation: Let f ( x ) = x sin x
f ( x ) = lim x 0 x sin x
f ( x ) = lim x 0 1 sin x x = lim x 0 1 lim x 0 ( sin x x ) = 1 1 = 1
Kylee Mathis

Kylee Mathis

Beginner2023-02-19Added 1 answers

Solution:
We must know the critical trigonometric limit:
lim x 0 sin x x = 1
Thus, we have that:
lim x 0 x sin x = lim x 0 ( sin x x ) - 1 = ( lim x 0 sin x x ) - 1 = 1 - 1 = 1

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