lim x → 0 x e 1 + x 2 + x 4 - 1 / x - 1 1 + x 2 + x 4 - 1

lim x → 0 e 1 + x 2 + x 4 − 1 x - 1 1 + x 2 + x 4 − 1 x p u t 1 + x 2 + x 4 − 1 x = t clearly x → 0 ⇒ t → 0 ∴ given limit = lim t → 0 e t − 1 t = 1

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsExponential and logarithmic limitsHard2 minPYQ_2020

MathematicsHardsingle choice

$\lim_{x \to 0} \frac{x (e^{(\sqrt{1 + x^{2} + x^{4}} - 1) / x} - 1)}{\sqrt{1 + x^{2} + x^{4}} - 1}$

Answer:

Solution:

$\lim_{x \to 0} \frac{(e^{\frac{\sqrt{1 + x^{2} + x^{4}} - 1}{x}} - 1)}{(\frac{\sqrt{1 + x^{2} + x^{4}} - 1}{x})}$

$p u t \frac{\sqrt{1 + x^{2} + x^{4}} - 1}{x} = t$

clearly $x \to 0 \Rightarrow t \to 0$

$∴$ given limit $= \lim_{t \to 0} \frac{e^{t} - 1}{t} = 1$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Exponential and logarithmic limits

⏱ 2mℹ️ Source: PYQ_2020

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