The values of $a$ and $b$ such that $\mathop {\lim }\limits_{x \to 0} \frac{{x\left( {1 + a\cos x} \right) - b\sin x}}{{{x^3}}} = 0$, are

JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

The values of

a

and

b

such that

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

, are

View answer and explanation

Correct option: C

- \frac{5}{2}, - \frac{3}{2}

Option C (

\frac{{ - 5}}{2}, - \frac{3}{2}

) is correct because by expanding the trigonometric functions using Taylor series and equating coefficients, the values of a and b can be determined.

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