$\mathop {\lim }\limits_{x \to 1} \frac{{\sqrt {1 - \cos 2\left( {x - 1} \right)} }}{{x - 1}}$

Exists and is equals $\sqrt 2 $

Exists and is equals $ - \sqrt 2 $

Does not exist because $x - 1 \to 0$

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Analyzing +4 | -1

\lim\limits_{x \to 1} \frac{{\sqrt {1 - \cos 2\left( {x - 1} \right)} }}{{x - 1}}

View answer and explanation

Correct option: D

Does not exist because left hand limit is not equal to right hand limit

Option A (

{\left( {\log a} \right)^2}

) is correct. Applying L'Hopital's rule twice gives the result

{\left( {\log a} \right)^2}

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f^{\prime}(0)

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