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Take the limit

  1. Feb 28, 2014 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=67104&stc=1&d=1393602574.png


    2. Relevant equations
    How does he get sin(theta)/theta / 1+ sintheta/theta *1/costheta
    I don't understand how he goes from sinetheta/theta + tantheta to sin(theta)/theta / 1+ sintheta/theta *1/costheta

    to me it looks like he just brought up the theta like theta/1 and just bumped up the theta but i know you cant do that.


    3. The attempt at a solution
    Ive tried too many times, there is my question if anyone can help. I appreciate it.
     

    Attached Files:

  2. jcsd
  3. Feb 28, 2014 #2
    1/theta was multiplied in both the numerator and denominator (i.e. Multiplying by 1). It's a type of algebraic manipulation trick, similar to cleverly adding 0 to an expression to simplify it.
     
  4. Feb 28, 2014 #3

    PeroK

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    Another method: you could try inverting the original limit and see what you get:

    [tex]\lim_{θ→0} \frac{θ+tanθ}{sinθ}[/tex]
     
  5. Feb 28, 2014 #4
    Thank you, I remember that trick. I don't see it though because if you times it by theta/theta wouldn't it be thetasin(theta)/ 2theta + tantheta? Even if i did (1/theta) / (1/theta) its seems not to work because 1/costheta would be 1/theta(cos(theta))..dang i dont see it.
     
  6. Feb 28, 2014 #5
    So i see that it would work for (1/theta)(1/theta) is that what you mean? i mean that is the same thing as theta over theta but you have to put it in that form for it to work
     
  7. Feb 28, 2014 #6

    Yeah, that's what I mean. The whole point of doing that is so you would have a ##\frac{sin(\theta)}{\theta}## in the expression, which you know the limit of.
     
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