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Continuity And Differentiability

Question
CBSEENMA12036094

limit as straight x space rightwards arrow 2 of space open parentheses fraction numerator square root of 1 minus cos space open curly brackets 2 left parenthesis straight x minus 2 right parenthesis close curly brackets end root over denominator straight x minus 2 end fraction close parentheses
  • does not exist

  • equal square root of 2

  • equal negative square root of 2

  • equal fraction numerator 1 over denominator square root of 2 end fraction

Solution

A.

does not exist

stack lim space with straight x space rightwards arrow 2 below square root of 2 space fraction numerator vertical line sin space left parenthesis straight x minus 2 right parenthesis vertical line over denominator left parenthesis straight x minus 2 right parenthesis end fraction
therefore does not exist

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