The value of lim x → 0 x ( 1 + x ) 1/ x − e is

( 1 + x ) x 1 = e x 1 l o g ( 1 + x ) = e ( 1 − 2 x + 3 x 2 − 4 x 3 …… )

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MathematicsLimitsStandard Limits (All types)Medium2 minQB

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The value of $lim_{x \to 0} \frac{( 1 + x ) ^{1/ x} - e}{x}$ is

Answer:

Solution:

$(1 + x)^{\frac{1}{x}} = e^{\frac{1}{x} l o g (1 + x)}$ $= e^{(1 - \frac{x}{2} + \frac{x ^{2}}{3} - \frac{x ^{3}}{4} \dots\dots)}$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Standard Limits (All types)

⏱ 2mℹ️ Source: QB

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