If a > 0 , b > 0 then lim n → ∞ ( a a − 1 + b n 1 ) n =

Let n 1 = x , ⇒ x → 0 as n → ∞ then required limit x → 0 Lt ( a a − 1 + b x ) x 1 = e Lt t x a b x − 1 = e a 1 l o g e b = ( b a 1 )

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MathematicsLimitsStandard Limits (All types)Easy2 minQB

MathematicsEasysingle choice

If $a > 0, b > 0$ then $lim_{n \to \infty} (\frac{a - 1 + b ^{\frac{1}{n}}}{a})^{n} =$

Answer:

Solution:

Let $\frac{1}{n} = x, \Rightarrow x \to 0$ as $n \to \infty$

then required limit

$x \to 0 Lt (\frac{a - 1 + b ^{x}}{a})^{\frac{1}{x}} = e^{Lt t ^{\frac{b ^{x} - 1}{x ^{a}}}}$

$= e^{\frac{1}{a} l o g e^{b}} = (b^{\frac{1}{a}})$

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

⏱ 2mℹ️ Source: QB

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