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is the limit as x approaches 0 of sin3x over 3x equal to zero?

sorry--
basically this is my problem:

lim [sin 3x / 4x)
x-> 0

~~~~I multiplied& eventually got to
.75* lim (sin 3x / 3x)
x-> 0

~so i figured since (lim (sinx/x)
x-> 0
was equal to zero, then

lim (sin3x/ 3x) also equaled 0
x-> 0

is that right? thank you !!!
(all of the x-> 0 should be under the "lim" -- just in case the text shifts...)

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3 answers

  1. see below

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  2. your preliminary steps are correct

    lim sin3x/(4x) as x--> 0
    = lim (3/4)(sin3x/(3x))
    = 3/4(1)
    = 3/4

    lim sinx/x = 1 not zero
    as x-->0

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  3. continued..

    Here is a simple way to check your limit answers if you have a calculator

    pick a value very "close" to your approach value, in this case I would pick x = .001
    evaluate using that value, (you are not yet dividing by zero, but close)
    for your question I got .749998875, close to 3/4 I would say.
    PS. Make sure your calculator is set to Radians

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