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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 2}\left(\frac{1}{x-2}-\frac{2}{x^2-2 x}\right)=$
  • A
    $\frac{1}{3}$
  • B
    $\frac{1}{4}$
  • C
    $\frac{1}{5}$
  • ✓
    $\frac{1}{2}$
✓

Answer

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

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