Best solutions to - "Find solution limx→0tan⁡x−sin⁡xx3" - Plainmath

SchachtN

Answered question

2020-12-24

Find solution

lim_{x \to 0} \frac{\tan x - \sin x}{x^{3}}

Answer & Explanation

Benedict

Skilled2020-12-25Added 108 answers

\tan (x) = x + \frac{x^{3}}{3} + 2 \frac{x^{5}}{15} + 17 \frac{x^{7}}{315} + \dots

\sin (x) = x - \frac{x^{3}}{3}! + \frac{x^{5}}{5}! - \frac{x^{7}}{7}! + \dots

\tan (x) - \sin (x) = x^{3} (\frac{1}{3} + \frac{1}{3}!) + x^{5} (\frac{2}{15} + \frac{1}{5}!) + x^{7} (\frac{17}{315} + \frac{1}{7}!) + \dots

f (x) = \frac{\tan (x) - \sin (x)}{x^{3}} = \frac{1}{2} + 17 \frac{x^{2}}{120} + 13 \frac{x^{4}}{240} + \dots

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