First slide

Introduction to limits

Question

$lim_{x \to \infty} \frac{\log x^{n} - [x]}{[x]}, where n \in N and [\cdot]$ denotes greatest integer function, is

Moderate

A

1
B

-1
C

0
D

none of these

Solution

We have,
$\begin{array}{l} lim_{x \to \infty} \frac{\log x^{n} - [x]}{[x]} \\ = lim_{x \to \infty} \frac{n \log x - [x]}{[x]} \\ = n lim_{x \to \infty} \frac{\log x}{[x]} - 1 = n \times 0 - 1 = - 1 \end{array}$

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