JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

\lim \limits_{{x \rightarrow 0}} \frac{\sin (\alpha x-\ln (1+\beta x))}{e^{3 x}-3 x-1}=1

, then

\alpha+2 \beta

is equal to

View answer and explanation

Correct option: C

Option C (9) is correct because by using L'Hopital's rule and series expansion, we find that

\alpha = \beta

and

\beta^2 = 9

, leading to

\alpha + 2\beta = 9

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