Q53 / 150 · MHT CET 2022 (07 Aug Shift 2) · Mathematics

$\lim _{x \rightarrow 0} \frac{2 x}{|x|+x^2}=$

  • A
    Limit exists
  • Correct answer
    B
    Limit does not exists
  • C
    $2$
  • D
    $-2$

Solution

$\lim _{x \rightarrow 0} \frac{2 x}{|x|+x^2}$ L.H.L $\lim _{x \rightarrow 0^{-}} \frac{2 x}{-x+x^2}=\lim _{x \rightarrow 0^{-}} \frac{2}{-1+x}=-\infty$ R.H.L $\lim _{x \rightarrow 0^{+}} \frac{2 x}{x+x^2}=\lim _{x \rightarrow 0^{+}} \frac{2}{1+x}=\infty$ $\because$ L.H.L $\neq$ R.H.L $\Rightarrow$ limit does not exist

Hence, the correct answer is option: 'B'.

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