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Homework Help: Lim x^3/(tan^3(2x)) x->0

  1. Apr 3, 2005 #1
    How do you start this problem?
    lim x^3/(tan^3(2x))
    x->0
     
  2. jcsd
  3. Apr 3, 2005 #2
    Use

    [tex]\tan{x} = \frac{\sin{x}}{\cos{x}}, \; \mbox{and} \ \lim_{x \rightarrow 0} \frac{\sin{\alpha x}}{\alpha x} = 1[/tex]
     
  4. Apr 3, 2005 #3
    how do you split tan^3(2x) into sin and cos?.....sin^3(2x)/cos^3(2x) or sin(2x)^3/cos(2x)^3??
     
  5. Apr 3, 2005 #4

    xanthym

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    Science Advisor

    [tex] 1): \ \ \ \ \tan^{3}(2x) \ = \ \frac {\sin^{3}(2x)} {\cos^{3}(2x)} [/tex]

    [tex] 2): \ \ \ \ \Longrightarrow \ \ \frac {x^{3}} { \tan^{3}(2x)} \ = \ \frac {\cos^{3}(2x)} { \frac {\sin^{3}(2x)} {x^{3}} } \ = \ \frac {\cos^{3}(2x)} { \frac {\sin^{3}(2x)} {(1/8) \cdot (2x)^{3}} } \ = \ \left( \frac{1}{8} \right) \cdot \left ( \frac {\cos^{3}(2x)} { \left ( \frac {\sin(2x)} {(2x)} \right )^{3} } \right ) [/tex]

    Now use info provided by Data in MSG #2 to evaluate required Limit.


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    Last edited: Apr 3, 2005
  6. Apr 3, 2005 #5
    thanks...^^
     
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