Limits tends to Trigonometry

Calculus Level 4

Evaluate lim ⁡ x → 0 tan ⁡ x + 4 tan ⁡ 2 x − 3 tan ⁡ 3 x x 2 tan ⁡ x \displaystyle \lim_{x\to0} \dfrac{\tan x + 4\tan 2x - 3\tan 3x}{x^2 \tan x} .


The answer is -16.

Deepanshu Dhruw by Deepanshu Dhruw , 21, India

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2 solutions

Deepanshu Dhruw
Jan 13, 2017

7 Helpful 0 Interesting 0 Brilliant 0 Confused
Prakhar Bindal
Jan 16, 2017

Relevant wiki: Limits by Taylor series

By Maclaurin's series of tanx = x+x^3/3+.............O(x^2)

substituting we get the required result

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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