lim-x-0-7tan-x-tan-7x-x-3-

Question Number 162523 by cortano last updated on 30/Dec/21

\lim_{x \to 0} \frac{7 \tan x - \tan 7 x}{x^{3}} = ?

Answered by Ar Brandon last updated on 30/Dec/21

L = \lim_{x \to 0} \frac{7 \tan x - \tan 7 x}{x^{3}}

= \lim_{x \to 0} \frac{7 (x + \frac{x^{3}}{3}) - (7 x + \frac{{(7 x)}^{3}}{3})}{x^{3}}

= \lim_{x \to 0} \frac{1}{x^{3}} (\frac{7 x^{3}}{3} - \frac{343 x^{3}}{3}) = \frac{7 - 343}{3} = - 112

Answered by bobhans last updated on 30/Dec/21

\lim_{x \to 0} \frac{7 \tan x - 7 x + 7 x - \tan 7 x}{x^{3}} =

\lim_{x \to 0} \frac{7 (\tan x - x)}{x^{3}} - 343 \lim_{x \to 0} \frac{\tan 7 x - 7 x}{{(7 x)}^{3}} =

\frac{7}{3} - \frac{343}{3} = - 112

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