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JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Mathematics
Chapter
Limits

JEE Main 2011 · Mathematics · Limits

_ x arrow 2 ( 1- \ 2(x-2)\ x-2 )

\lim _{x \rightarrow 2} \left(\frac{\sqrt{1-cos⁡{2(x−2)}\cos \{2(x-2)\}}}{x-2}\right)

Options

  1. Aequals 2\sqrt{2}
  2. Bequals −2-\sqrt{2}
  3. Cequals 12\frac{1}{\sqrt{2}}
  4. Ddoes not exist

Correct answer

D. does not exist

Step-by-step solution

lim⁡x→22sin⁡2(x−2)x−2lim⁡x→22∣sin⁡(x−2)∣x−2 R.H.L. =2, L.H.L. =−2\begin{aligned}& \lim _{x \rightarrow 2} \frac{\sqrt{2 \sin ^2(x-2)}}{x-2}\\ & \lim _{x \rightarrow 2} \frac{\sqrt{2}|\sin (x-2)|}{x-2}\\ & \text{ R.H.L. }=\sqrt{2}, \text{ L.H.L. }=-\sqrt{2} \end{aligned}Limit does not exist.
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