First slide

Introduction to limits

Question

If a >0, $\lim_{x \to \infty} \frac{[a x + b]}{x}$ is [where [ . ] denotes G.I.F ]

Moderate

A

0
B

1
C

a
D

b

Solution

$u s e s a n d w i t c h t h e o r e m a x + b - 1 < [a x + b] \leq a x + b \lim_{x \to \infty} (a + \frac{b}{x} - \frac{1}{x}) < \lim_{x \to \infty} \frac{[a x + b]}{x} < \leq \lim_{x \to \infty} (a + \frac{b}{x}) \Rightarrow a$

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