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Simple Limit of a Trigonmetric Function

  1. Apr 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the limit algebraically.
    lim x--> 0 sin (x)/3x


    2. Relevant equations

    lim x--> 0 (sin x)/x = 1

    3. The attempt at a solution
    I tried multiplying both sides by (3/3) and got and answer of (1/3).
    But if I multiply sin (x) by 3, is that the same thing as sin (3x) ?
     
    Last edited: Apr 4, 2009
  2. jcsd
  3. Apr 4, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    But if I multiply sin (x) by 3, is that the same thing as sin (3x) ?

    No. In that case the answer would be 1, which is wrong.
     
  4. Apr 5, 2009 #3
    Okay, so how do I do it?
     
  5. Apr 5, 2009 #4
    if you know that

    [tex]
    \lim_{x\rightarrow 0} \frac{\sin(x)}{x} = 1
    [/tex]

    but given is

    [tex]
    \lim_{x\rightarrow 0} \frac{\sin(x)}{3x}
    [/tex]

    you, probably, have to rearrange the given expression to turn it or a part of the given expression into the form of the formula. How would you do that?
     
  6. Apr 5, 2009 #5
    You had a right idea here, but executed it a little wrong. To get from [itex]\sin x/x[/itex] to [itex]\sin x/(3x)[/itex] you don't multiply by 3/3. You multiply/divide by...

    Also, there is also the property that if [itex]\lim_{x\to a} f(x)[/itex] exists, then
    [tex] \lim_{x\to a} \left[ cf(x) \right] = c \lim_{x\to a} f(x) [/tex]
     
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