lim x → 0 ( 1 + 3 x 1 + 2 x ) x 2 1 ⋅ e x 1 = ____

lim x → 0 e x 2 1 ( l o g ( 1 + 2 x ) − l o g ( 1 + 3 x ) + x 1 e l i m x → 0 x 2 ( l o g ( 1 + 2 x ) − l o g ( 1 + 3 x ) + x = e 2 5

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsStandard Limits (All types)Medium2 minQB

MathematicsMediumsingle choice

$lim_{x \to 0} (\frac{1 + 2 x}{1 + 3 x})^{\frac{1}{x ^{2}}} \cdot e^{\frac{1}{x}} =$ $____$

Answer:

Solution:

$lim_{x \to 0} e^{\frac{1}{x ^{2}} (l o g (1 + 2 x) - l o g (1 + 3 x) + \frac{1}{x}}$

$e^{l i m_{x \to 0} \frac{( l o g ( 1 + 2 x ) - l o g ( 1 + 3 x ) + x}{x ^{2}}} = e^{\frac{5}{2}}$

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

⏱ 2mℹ️ Source: QB

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