x → 0 Lt ( x s i n h x ) x 2 1

Let l = Lt x → 0 ( x s i n h x ) x 2 1 lo g l = Lt x → 0 x 2 1 lo g ( x s i n h x ) by L ′ Hospital Rule ⇒ l = e 6 1

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsExponential and logarithmic limitsMedium2 minQB

MathematicsMediumsingle choice

$x \to 0 Lt (\frac{s i n h x}{x})^{\frac{1}{x ^{2}}}$

Answer:

Solution:

Let $l = Lt_{x \to 0} (\frac{s i n h x}{x})^{\frac{1}{x ^{2}}}$

$lo g l = Lt_{x \to 0} \frac{1}{x ^{2}} lo g (\frac{s i n h x}{x}) by L^{'} Hospital Rule \Rightarrow l = e^{\frac{1}{6}}$

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

⏱ 2mℹ️ Source: QB

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