GATE | GATE CS Mock 2018 | Set 2 | Question 52

Find the value of
\lim_{x\rightarrow 0}\frac{tanx-x}{x^3}
(A) 1/3
(B) -1/6
(C) 1/2
(D) None of these

Answer: (A)

Explanation: Option (A) is correct.
L1=\lim_{x\rightarrow 0}\frac{tanx-x}{x^3} \newline \newline L1=\lim_{x\rightarrow 0}\frac{tan2x-2x}{8x^3} \newline \newline 4L1=\lim_{x\rightarrow 0}\frac{\frac{1}{2}tan2x-2x}{x^3} \newline \newline 3L1=\lim_{x\rightarrow 0}\frac{\frac{1}{2}tan2x-2x}{x^3} \newline \newline =\ \ \  \lim_{x\rightarrow 0}\frac{tanx}{x}\frac{\frac{1}{1-tan^2x}-1}{x^2} \newline \newline L1=\lim_{x\rightarrow 0}\frac{(tanx)^3}{x^3}=1 \newline \newline L1=\frac{1}{3}

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