Results 1 to 11 of 11

Math Help - How To Find The Limits Algebraically...?

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    123

    How To Find The Limits Algebraically...?

    lim ((sin^2)x)/x
    x->0

    This is a tricky question... Can anybody lend a helping hand?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by AlphaRock View Post
    lim ((sin^2)x)/x
    x->0

    This is a tricky question... Can anybody lend a helping hand?
    \lim_{x\to{0}}\frac{\sin^2(x)}{x}=\lim_{x\to{0}}\f  rac{\sin(x)}{x}\cdot \sin(x)=\dots

    You should know what \lim_{x\to{0}}\frac{\sin(x)}{x} equals.

    Does this make sense?

    --Chris
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2008
    Posts
    123
    Quote Originally Posted by Chris L T521 View Post
    \lim_{x\to{0}}\frac{\sin^2(x)}{x}=\lim_{x\to{0}}\f  rac{\sin(x)}{x}\cdot \sin(x)=\dots

    You should know what \lim_{x\to{0}}\frac{\sin(x)}{x} equals.

    Does this make sense?

    --Chris
    Thanks, Chris.

    What I can't understand is why

    lim ((sin^2)x)/x
    x->0

    will equal...

    lim (sinx)/x times sin(x)
    x->0
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie kirbyiwaki's Avatar
    Joined
    Sep 2008
    Posts
    10
    \lim_{x\to{0}}\frac{\sin^2(x)}{x}=\lim_{x\to{0}}\f  rac{\sin(x)}{x}\cdot \sin(x)

    Just factorize the

    \sin^2(x)

    into

    \sin(x)\cdot\sin(x)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by AlphaRock View Post
    Thanks, Chris.

    What I can't understand is why

    lim ((sin^2)x)/x
    x->0

    will equal...

    lim (sinx)/x times sin(x)
    x->0
    Because \sin^2(x)=[\sin(x)]^2=\sin(x) \times \sin(x)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Apr 2008
    Posts
    123
    Ah! I understand why now...

    Thanks, guys.

    I'm having trouble with this new limit question:

    lim ((1/(2+x)) - (1/2))/x
    x->0


    P.S. How do you guys format stuff like this (I just copy and pasted):


    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Quote Originally Posted by AlphaRock View Post
    Ah! I understand why now...

    Thanks, guys.

    I'm having trouble with this new limit question:

    lim ((1/(2+x)) - (1/2))/x
    x->0


    P.S. How do you guys format stuff like this (I just copy and pasted):



    Is this what it looks like?

    \lim_{x \to 0} \frac{\frac{1}{2+x} - \frac{1}{2}}{x}
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Apr 2008
    Posts
    123
    Quote Originally Posted by 11rdc11 View Post
    Is this what it looks like?

    \lim_{x \to 0} \frac{\frac{1}{2+x} - \frac{1}{2}}{x}
    Yup!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    \lim_{x \to 0} \frac{\frac{1}{2+x} - \frac{1}{2}}{x}

    Find common denominator in the numerator

    \lim_{x \to 0} \frac{\frac{2-2-x}{2(2+x)}}{x} = \frac{\frac{-x}{4+2x}}{x} = \frac{-x}{x(4+2x)}


    which equals

    \lim_{x \to 0}~\frac{-1}{4+2x}~=~\frac{-1}{4}
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Member
    Joined
    Apr 2008
    Posts
    123
    Quote Originally Posted by 11rdc11 View Post
    \lim_{x \to 0} \frac{\frac{1}{2+x} - \frac{1}{2}}{x}

    Find common denominator in the numerator

    \lim_{x \to 0} \frac{\frac{2-2-x}{2(2+x)}}{x} = \frac{\frac{-x}{4+2x}}{x} = \frac{-x}{x(4+2x)}


    which equals

    \lim_{x \to 0}~\frac{-1}{4+2x}~=~\frac{-1}{4}
    Can somebody explain this?

    \frac{\frac{-x}{4+2x}}{x} = \frac{-x}{x(4+2x)}

    Because I'm having troubles understanding how you got there...
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by AlphaRock View Post
    Can somebody explain this?

    \frac{\frac{-x}{4+2x}}{x} = \frac{-x}{x(4+2x)}

    Because I'm having troubles understanding how you got there...
    \frac{\frac{-x}{4+2x}}{x} =\frac{\frac{-x}{4+2x}}{1}\cdot\frac{1}{x} = \frac{-x}{4+2x}\cdot\frac{1}{x} =\frac{-x}{x(4+2x)}

    Does this make sense?

    --Chris
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the limit algebraically
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 20th 2011, 08:28 PM
  2. Replies: 1
    Last Post: October 28th 2010, 04:28 AM
  3. algebraically find arcsine?
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: October 18th 2010, 04:36 PM
  4. Find Delta's Algebraically
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 22nd 2009, 11:55 AM
  5. Algebraically find the coordinates.
    Posted in the Algebra Forum
    Replies: 4
    Last Post: October 2nd 2008, 02:06 AM

Search Tags


/mathhelpforum @mathhelpforum