The value of $\mathop {\lim }\limits_{x \to 0} \frac{{1 + \sin x - \cos x + \log \left( {1 - x} \right)}}{{{x^3}}}$ is

JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

The value of

\lim\limits_{x \to 0} \frac{{1 + \sin x - \cos x + \log \left( {1 - x} \right)}}{{{x^3}}}

View answer and explanation

Correct option: C

- \frac{1}{2}

Option C (-

\frac{1}{2}

) is correct because using Taylor series expansions for the trigonometric and logarithmic functions, the limit evaluates to -

\frac{1}{2}

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