Evaluating \lim_{x \to 0} \frac{x-\tan^{-1} x}{x \sin x}

Emmy Combs

Emmy Combs

Answered question

2022-01-23

Evaluating limx0xtan1xxsinx

Answer & Explanation

sineurosi0f

sineurosi0f

Beginner2022-01-24Added 14 answers

limx0xarctanxx2limx0xsinx
Now apply L’Hôpital for the first limit.
Allison Compton

Allison Compton

Beginner2022-01-25Added 16 answers

Use Taylor expansion:
limx0xtan1xxsinx=limx0x(xx33+x55+O(x7))xsinx=
limx0x(x3x35+O(x5))sinx=0

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