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

By using sandwich theorem
Since f is increasing function
$\begin{array}{l} = f (x) < f (2 x) < f (3 x) \\ = \frac{f (x)}{f (x)} < \frac{f (2 x)}{f (x)} < \frac{f (3 x)}{f (x)} \\ = \lim_{x \to 0} \frac{f (x)}{f (x)} < \lim_{x \to 0} \frac{f (2 x)}{f (x)} < \lim_{x \to 0} \frac{f (3 x)}{f (x)} \\ = 1 < \lim_{x \to 0} \frac{f (2 x)}{f (x)} < 1 \\ f r o m s a n d w i t c h t h e r o m \\ \lim_{x \to 0} \frac{f (2 x)}{f (x)} = 1 \end{array}$

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