lim x → 0 3 x 2 + 2 7 x 2 + 2 1 x 2 is equal to

Let L = l i m x → 0 3 x 2 + 2 7 x 2 + 2 1 x 2 = e lim x → 0 1 x 2 3 x 2 + 2 7 x 2 + 2 - 1 = e lim x → 0 - 4 x 2 7 x 2 + 2 = e - 4 2 = e - 2 = 1 e 2

Mathematics - Limits Question with Solution | TestHub

MathematicsLimits1 power infinty basedEasy2 minPYQ_2020

MathematicsEasysingle choice

$\lim_{x \to 0} {(\frac{3 x^{2} + 2}{7 x^{2} + 2})}^{\frac{1}{x^{2}}}$ is equal to

Answer:

Solution:

Let $L = \underset{x \to 0}{l i m} {(\frac{3 x^{2} + 2}{7 x^{2} + 2})}^{\frac{1}{x^{2}}}$

$= e^{\lim_{x \to 0} \frac{1}{x^{2}} \{\frac{3 x^{2} + 2}{7 x^{2} + 2} - 1\}}$

$= e^{\lim_{x \to 0} \{\frac{- 4 x^{2}}{7 x^{2} + 2}\}}$

$= e^{\frac{- 4}{2}}$

$= e^{- 2}$

$= \frac{1}{e^{2}}$

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

⏱ 2mℹ️ Source: PYQ_2020

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