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Question: If \(\lim_{x \rightarrow 0}\frac{3\tan^{- 1}x + 3\tan x - x^{5} - 6x}{3x^{n}}\) is a finite number t...

If lim⁡x→03tan⁡−1x+3tan⁡x−x5−6x3xn\lim_{x \rightarrow 0}\frac{3\tan^{- 1}x + 3\tan x - x^{5} - 6x}{3x^{n}} is a finite number then the greatest value of n is

A

3

B

5

C

2

D

None of these

Answer

None of these

Explanation

Solution

lim⁡x→0\lim_{x \rightarrow 0}

[(3x−x3+35x5−...)+(3x+x3+25x5+...)−6x−x5]xn\frac{\left\lbrack \left( 3x - x^{3} + \frac{3}{5}x^{5} - ... \right) + \left( 3x + x^{3} + \frac{2}{5}x^{5} + ... \right) - 6x - x^{5} \right\rbrack}{x^{n}}

all coff. of x, x3 and x5 is zero and minimum power of x occurs in numerator is 7

So n = 7