Results 1 to 6 of 6

Math Help - Help With Trig Limit

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    29

    Help With Trig Limit

    How do you solve the limit: lim x --> 0 sin (9x)/ sin(5x)

    I really don't have much of a clue where to start, so if someone could explain every step of how to solve this, I'd be real grateful.
    Last edited by zerobladex; September 28th 2009 at 05:52 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member apcalculus's Avatar
    Joined
    Apr 2009
    From
    Boston
    Posts
    293
    Quote Originally Posted by zerobladex View Post
    How do you solve the limit: sin (9x)/ sin(5x)

    I really don't have much of a clue where to start, so if someone could explain every step of how to solve this, I'd be real grateful.
    Where is x going towards in this problem?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    as x\to0, otherwise what'd be the sense on taking other value.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member DeMath's Avatar
    Joined
    Nov 2008
    From
    Moscow
    Posts
    473
    Thanks
    5
    Quote Originally Posted by zerobladex View Post
    How do you solve the limit: lim x --> 0 sin (9x)/ sin(5x)

    I really don't have much of a clue where to start, so if someone could explain every step of how to solve this, I'd be real grateful.
    Hint

    \mathop {\lim }\limits_{x \to 0} \frac{{\sin 9x}}<br />
{{\sin 5x}} = \frac{9}<br />
{5} \cdot \mathop {\lim }\limits_{x \to 0} \frac{{\sin 9x}}<br />
{{9x}} \cdot {\left( {\mathop {\lim }\limits_{x \to 0} \frac{{\sin 5x}}<br />
{{5x}}} \right)^{ - 1}} =  \ldots
    Last edited by DeMath; September 28th 2009 at 06:14 PM. Reason: typo!!!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Oct 2008
    Posts
    29
    What I'm kind of confused on is how u factored out the 5/9 form the sin (x) equations. Could you please explain that?

    Oh wait! Is the sin 9x/ 9x thing taken from the sin (x)/ x is equal to 1? But then don't you have to multiply the top and bottom both by 9x in order for it to remain equivalent? Same with the 5x?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member DeMath's Avatar
    Joined
    Nov 2008
    From
    Moscow
    Posts
    473
    Thanks
    5
    Quote Originally Posted by zerobladex View Post
    What I'm kind of confused on is how u factored out the 5/9 form the sin (x) equations. Could you please explain that?

    Oh wait! Is the sin 9x/ 9x thing taken from the sin (x)/ x is equal to 1? But then don't you have to multiply the top and bottom both by 9x in order for it to remain equivalent? Same with the 5x?
    \mathop {\lim }\limits_{x \to 0} \frac{{\sin 9x}}<br />
{{\sin 5x}} = \frac{9}<br />
{5} \cdot \mathop {\lim }\limits_{x \to 0} \left[ {\frac{{\sin 9x}}<br />
{{9x}} \cdot \frac{{5x}}<br />
{{\sin 5x}}} \right] =

    = \frac{9}<br />
{5} \cdot \mathop {\lim }\limits_{x \to 0} \frac{{\sin 9x}}<br />
{{9x}} \cdot \mathop {\lim }\limits_{x \to 0} \frac{{5x}}<br />
{{\sin 5x}} =

    = \frac{9}<br />
{5} \cdot \mathop {\lim }\limits_{x \to 0} \frac{{\sin 9x}}<br />
{{9x}} \cdot {\left( {\mathop {\lim }\limits_{x \to 0} \frac{{\sin 5x}}<br />
{{5x}}} \right)^{ - 1}} =  \ldots

    Now use this

    {\color{red}\boxed{{\color{black}\mathop {\lim }\limits_{x \to 0} \frac{{\sin ax}}{{ax}} = 1}}}
    Last edited by DeMath; September 28th 2009 at 06:55 PM. Reason: typo!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig Limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 2nd 2008, 04:20 PM
  2. Trig limit
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 20th 2008, 07:39 PM
  3. trig. limit
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 9th 2008, 10:15 PM
  4. Limit of trig?
    Posted in the Calculus Forum
    Replies: 13
    Last Post: June 2nd 2008, 06:11 PM
  5. Trig Limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 21st 2007, 06:16 AM

Search Tags


/mathhelpforum @mathhelpforum