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Homework Help: Find the limit.

  1. Feb 6, 2008 #1
    lim y->0 (sin 3y * cot 5y)/(y * cot 4y)

    Tricky problem to me. I understand what to do if the problem was something like sin 5x / 4x.
    Last edited: Feb 6, 2008
  2. jcsd
  3. Feb 6, 2008 #2
    Well first rewrite cot in terms of sin and cosine, and look to come up with something sinx/x when x-->0 to some parts of it at least.
  4. Feb 6, 2008 #3
    [tex]\lim_{y\rightarrow 0}\frac{\sin{3y}\cot{5y}}{y\cot{4y}}[/tex]
  5. Feb 6, 2008 #4
    Correct. Sorry I'm not good at latex.
  6. Feb 6, 2008 #5
    [tex]\lim_{y\rightarrow 0}\frac{\sin{3y}}{y}\cdot\frac{\sin{4y}}{\cos{4y}}\cdot\frac{\cos{5y}}{\sin{5y}}[/tex]

    How can you manipulate your limit? The left term is very easy.
    Last edited: Feb 7, 2008
  7. Feb 6, 2008 #6
    I know what to do now.
  8. Feb 7, 2008 #7


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    It would be easier if it were sin(3y)/y rather than sin(3x)/y !!!
  9. Feb 7, 2008 #8
    It was a typo!!!
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