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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow \infty}\left(\frac{x^3}{3 x^2-4}-\frac{x^2}{3 x+2}\right)$ is equal to
  • A
    $\frac{-1}{4}$
  • B
    $\frac{-1}{2}$
  • C
    $0$
  • ✓
    $\frac{2}{9}$
✓

Answer

Correct option: D.
$\frac{2}{9}$
(D)
$\lim _{x \rightarrow \infty}\left(\frac{x^3}{3 x^2-4}-\frac{x^2}{3 x+2}\right)$
$=\lim _{x \rightarrow \infty}\left[\frac{3 x^4+2 x^3-3 x^4+4 x^2}{\left(3 x^2-4\right)(3 x+2)}\right]$
$=\lim _{x \rightarrow \infty} \frac{2 x^2(x+2)}{\left(3 x^2-4\right)(3 x+2)}$
$=\lim _{x \rightarrow \infty} \frac{2\left(1+\frac{2}{x}\right)}{\left(3-\frac{4}{x^2}\right)\left(3+\frac{2}{x}\right)}=\frac{2}{9}$

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