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Lim x→0(sin x-xcos x)/(x^3 equals Single correct option
lim x → 0 sin x − x cos x x 3 \displaystyle\lim_{x\to0}\frac{\sin x-x\cos x}{x^3} x → 0 lim x 3 sin x − x cos x equals
A. 1 6 \frac16 6 1 B. 1 3 \frac13 3 1 C. 1 2 \frac12 2 1 D. 0 0 0 Show answer and solution Answer: (B) 1 3 \frac13 3 1
Use
sin x = x − x 3 6 + … \sin x=x-\frac{x^3}{6}+\dots sin x = x − 6 x 3 + … and
x cos x = x − x 3 2 + … x\cos x=x-\frac{x^3}{2}+\dots x cos x = x − 2 x 3 + … . The numerator is
x 3 2 − x 3 6 = x 3 3 \frac{x^3}{2}-\frac{x^3}{6}=\frac{x^3}{3} 2 x 3 − 6 x 3 = 3 x 3 , so the limit is
1 3 \frac13 3 1 . Replacing both terms by
x x x gives the wrong value
0 0 0 , since the leading terms cancel.
Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake