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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 2} \frac{|x-2|}{x-2}=$
  • A
    1
  • B
    -1
  • ✓
    does not exist
  • D
    2
✓

Answer

Correct option: C.
does not exist
(C)
$\lim _{x \rightarrow 2^{-}} \frac{|x-2|}{x-2}=\lim _{ h \rightarrow 0} \frac{|2- h -2|}{2- h -2}=-1$
and $\lim _{x \rightarrow 2^{+}} \frac{|x-2|}{x-2}=\lim _{h \rightarrow 0} \frac{|2+h-2|}{2+h-2}=1$
Hence, limit does not exist.

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