# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Wed, 19 Jun 2013 21:10:39 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 8 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Limits with trigonometric functionsPosted: Fri, 24 Feb 2012 17:42:08 UTC
 Senior Member

Joined: Sun, 25 Dec 2011 00:28:25 UTC
Posts: 95
Hello

Attempted:

Actually I haven't done much, just not to say nothing at all, could be simple, but since I hate trig...

Top

 Post subject: Re: Limits with trigonometric functionsPosted: Fri, 24 Feb 2012 18:17:45 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 23 Jun 2003 17:34:53 UTC
Posts: 2084
Location: San Antonio,Texas USA
A series expansion will work, or you can use .

_________________
Live long and prosper.

Top

 Post subject: Re: Limits with trigonometric functionsPosted: Fri, 24 Feb 2012 19:48:26 UTC
 Senior Member

Joined: Sun, 25 Dec 2011 00:28:25 UTC
Posts: 95
royhaas wrote:
A series expansion will work, or you can use .

Ufff...All I can do is to change numerator into:

I feel dumb. Still don't know what to do next any further step?

Top

 Post subject: Re: Limits with trigonometric functionsPosted: Fri, 24 Feb 2012 22:37:30 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7962
Location: Lexington, MA
Hello, kreshnik!

Quote:

. .

Multiply by

Multiply by

. . . . . . . . . . . . . .

Top

 Post subject: Re: Limits with trigonometric functionsPosted: Fri, 24 Feb 2012 22:43:12 UTC
 Senior Member

Joined: Sun, 25 Dec 2011 00:28:25 UTC
Posts: 95
Soroban wrote:
Hello, kreshnik!

Quote:

. .

Multiply by

Multiply by

. . . . . . . . . . . . . .

Many thanks, I'm speechless. Thank you

Top

 Post subject: Re: Limits with trigonometric functionsPosted: Fri, 24 Feb 2012 23:18:27 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Fri, 1 Jul 2011 01:17:26 UTC
Posts: 329
An alternate approach using first order approximations. cos(x) â‰ˆ 1 - (x^2)/2.
From this âˆšcos(x) â‰ˆ 1 - (x^2)/4 and numerator â‰ˆ -(x^2)/4, so limit = -1/4.

Top

 Post subject: Re: Limits with trigonometric functionsPosted: Sat, 25 Feb 2012 03:07:55 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6068
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
kreshnik wrote:
royhaas wrote:
A series expansion will work, or you can use .

Ufff...All I can do is to change numerator into:

I feel dumb. Still don't know what to do next any further step?

Split the fractions up. No need to multiply by :

_________________

Top

 Post subject: Re: Limits with trigonometric functionsPosted: Sat, 25 Feb 2012 06:33:27 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 21 May 2003 04:27:18 UTC
Posts: 996
outermeasure wrote:
Split the fractions up. No need to multiply by :

I agree...no need to encumber yourself with more algebra than necessary.
Remember to change variables in the second limit: , etc.

_________________
"Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another." Bernard Le Bovier Fontenelle (1657-1757)

"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy."
G.H. Hardy (1877-1947)

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 8 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous