First slide

Introduction to limits

Question

$If a, b, c, d are positive real numbers then Lt {(1 + \frac{1}{a + b n})}^{c + d n} =$

Moderate

A

$e^{\frac{d}{b}}$
B

$e^{\frac{c}{a}}$
C

$e^{\frac{c + d}{a + b}}$
D

$e$

Solution

$\underset{n \to \infty}{L t} {(1 + \frac{1}{a + b n})}^{c + d n} = {[\underset{n \to \infty}{L t} {(1 + \frac{1}{a + b n})}^{a + b n}]}^{\frac{c + d n}{a + b n}} = e^{d / b} .$

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