First slide

Introduction to limits

Question

If $m, n \in N, lim_{x \to 0} \frac{\sin x^{n}}{(\sin x)^{m}}$ is

Moderate

A

1,if n=m
B

0,if n>m
C

∞, if n < m
D

n/m, if n < m

Solution

$L = lim_{x \to 0} \frac{\sin x^{n}}{(\sin x)^{m}} = lim_{x \to 0} \frac{\frac{\sin x^{n}}{x^{n}} x^{n}}{\frac{(\sin x)^{m}}{x^{m}} x^{m}} = lim_{x \to 0} x^{n - m}$
If n=m, then
L=( a very small value near to zero )^{exactly zero} =1
If n>m, then
L= (a very small value near to zero)^{positive integer} =0
If n<m, then
L=(a very small value near to zero)^{negative integer} = ∞

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