First slide

Introduction to limits

Question

$The value of \lim_{x \to \infty} \{[\frac{100 x}{\sin x}] + [\frac{99 \sin x}{x}]\}, where [] represents the$ greatest integer function, is

Moderate

A

199
B

198
C

1
D

0

Solution

$\forall x > 0; \frac{x}{\sin x} > 1 a n d \forall x < 0; \frac{\sin x}{x} < 1$
$\begin{array}{l} \frac{x}{\sin x} > 1 and \frac{\sin x}{x} < 1 \\ \Rightarrow \frac{100 x}{\sin x} > 100 and \frac{99 \sin x}{x} < 99 \\ [\frac{100 x}{\sin x}] = 100, [\frac{99 \sin x}{x}] = 98 \end{array}$

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