First slide

Introduction to limits

Question

Let $f : R \to R$ be a positive increasing function with $\lim_{x \to \infty} \frac{f (3 x)}{f (x)} = 1,$ then $\lim_{x \to \infty} \frac{f (2 x)}{f (x)} =$

Moderate

A

$\frac{2}{3}$
B

$\frac{3}{2}$
C

3
D

1

Solution

$\sin c e f i s a n i n c r e a \sin g f u n c t i o n \Rightarrow f (x) \leq f (2 x) \leq f (3 x) \Rightarrow 1 \leq \frac{f (2 x)}{f (x)} \leq \frac{f (3 x)}{f (x)} \Rightarrow 1 \leq \lim_{x \to \infty} \frac{f (2 x)}{f (x)} \leq \lim_{x \to \infty} \frac{f (3 x)}{f (x)} \Rightarrow 1 \leq \lim_{x \to \infty} \frac{f (2 x)}{f (x)} \leq 1 b y s a n d w i t c h t h e o r e m \lim_{x \to \infty} \frac{f (2 x)}{f (x)} = 1$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App