JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

Let

f(\cdot)

and

g(\cdot)

be differentiable functions on

(-\infty

\infty)

and let

f^{\prime}(\cdot)

and

g^{\prime}(\cdot)

denote derivatives of

f(\cdot)

and

g(\cdot)

respectively. If

f(0)=\frac{1}{2}, g(0)=\frac{1}{3}, f^{\prime}(0)=1

and

g^{\prime}(0)=2

, then the value of

\lim \limits_{{x \rightarrow 0}} \frac{2 f\left(2 x^2+3 x\right)-1}{3 g(x)-1}

View answer and explanation

Correct option: A

Option A (1) is correct because the limit is evaluated using L'Hopital's rule and the given derivative values.

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