If lim x → ∞ ⁡ 1 + a x - 4 x 2 2 x = e 3 , then a is equal to

lim x → ∞ 1 + a x - 4 x 2 2 x ( 1 ∞ form ) = e lim x → ∞ ⁡ 1 + a x - 4 x 2 - 1 2 x = e lim x → ∞ ⁡ 2 a - 8 x = e 2 a ∴ e 2 a = e 3 ⇒ 2 a = 3 ⇒ a = 3 2

Home
PYQ PracticeFree
JEE Rank Predictor
Answer Key

Mathematics - Limits Question with Solution | TestHub

MathematicsLimits1 power infinty basedMedium2 minPYQ_2016

MathematicsMediumsingle choice

If $\lim_{x \to \infty} {(1 + \frac{a}{x} - \frac{4}{x^{2}})}^{2 x} = e^{3}$ , then $a$ is equal to

Options:

Answer:

Solution:

$\lim_{x \to \infty} {(1 + \frac{a}{x} - \frac{4}{x^{2}})}^{2 x}$ $(1^{\infty}$ form $)$

$= e^{[\lim_{x \to \infty} (1 + \frac{a}{x} - \frac{4}{x^{2}} - 1) 2 x]}$

$= e^{\lim_{x \to \infty} (2 a - \frac{8}{x}) = e^{2 a}}$

$∴$ $e^{2 a} = e^{3}$

$\Rightarrow 2 a = 3$

$\Rightarrow a = \frac{3}{2}$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:1 power infinty based

⏱ 2mℹ️ Source: PYQ_2016

Doubts & Discussion

Loading discussions...