Home » Ask & Discuss » Mathematics
« Back to Discussion

Differential Calculus

Blazing goIITian

Joined:	1 Apr 2012
Post:	381

19 May 2012 21:43:53 IST

0 People liked this

237

limit (conceptual)

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Differential Calculus

evalute limx->0 [ln(1+(sin^2)*x)cot ln^2 (1+x)] using LH rule ans=1

Comments (1)

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7958

19 May 2012 22:22:17 IST

Like 0 people liked this

$\lim_{x \to 0 }ln(1+sin^2x)cot(ln^2(1+x))$

$=\lim_{x \to 0 }\frac{ln(1+sin^2x)}{tan(ln^2(1+x))}$

$=\lim_{x \to 0 }\frac{sin^2x}{ln^2(1+x)}\; (since\; ln(1+x)\approx\ x; and\; sinx\approx x\; as\; x \to0)$

$=\lim_{x \to 0 }\frac{sin^2x}{x^2}\; (since\; ln(1+x)\approx\ x\; as\; x \to0)$

$=1$

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

Free Sign Up!

Preparing for JEE?

Kickstart your preparation with new improved study material - Books & Online Test Series for JEE 2014/ 2015

@ INR 4,950/-

For Quick Info

Name

Mobile

E-mail

City

Class

Find Posts by Topics

Physics

Topics

10271

20997

3868

2300

8075

2968

2790

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone

Sponsored Ads

Vertical Limit

Top Contributors

All Time This Month Last Week

Bipin Dubey

Altitude -	16545 m
Post -	7958

Himanshu

Altitude -	10925 m
Post -	3836

Hari Shankar

Altitude -	9960 m
Post -	2185

edison

Altitude -	10815 m
Post -	7797

Sagar Saxena

Altitude -	8625 m
Post -	8064

Yagyadutt Mishr..

Altitude -	6330 m
Post -	1979

35,229,755
Engineering Questions Attempted

6,69,530
Visitors Monthly

79
Engg. Exam Covered

5572
Students Currently Online

Connect with Us

Vriti Communities