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NDA 2017 Maths · Mathematics · Limits · medium

Lim x→∞(√(4x^2+3x)-2x) equals

Single correct option

lim⁡x→∞(4x2+3x−2x)\displaystyle\lim_{x\to\infty}\left(\sqrt{4x^2+3x}-2x\right) equals
  1. A. 32\frac32
  2. B. 34\frac34
  3. C. 00
  4. D. 33
Show answer and solution

Answer: (B) 34\frac34

Rationalise: 3x4x2+3x+2x=34+3/x+2→34\frac{3x}{\sqrt{4x^2+3x}+2x}=\frac{3}{\sqrt{4+3/x}+2}\to\frac34. The value 00 treats 4x2+3x≈2x\sqrt{4x^2+3x}\approx2x as exact, and 32\frac32 forgets that the denominator tends to 2+2=42+2=4, not 22.
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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