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Lim x→0(e^2x-1-2x)/(x^2 equals Single correct option
lim x → 0 e 2 x − 1 − 2 x x 2 \displaystyle\lim_{x\to0}\frac{e^{2x}-1-2x}{x^2} x → 0 lim x 2 e 2 x − 1 − 2 x equals
A. 0 0 0 B. 2 2 2 C. 1 1 1 D. 4 4 4 Show answer and solution Answer: (B) 2 2 2
Expand
e 2 x = 1 + 2 x + ( 2 x ) 2 2 + ⋯ = 1 + 2 x + 2 x 2 + … e^{2x}=1+2x+\frac{(2x)^2}{2}+\dots=1+2x+2x^2+\dots e 2 x = 1 + 2 x + 2 ( 2 x ) 2 + ⋯ = 1 + 2 x + 2 x 2 + … , so the numerator is
2 x 2 + … 2x^2+\dots 2 x 2 + … and the limit is
2 2 2 . Using
e 2 x − 1 2 x → 1 \frac{e^{2x}-1}{2x}\to1 2 x e 2 x − 1 → 1 only gives
1 1 1 for a different expression, and
4 4 4 forgets the
1 2 \frac12 2 1 in the series.
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