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Math Help - To Evaluate the following limit...

  1. #1
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    To Evaluate the following limit...

    I need some help in a problem from Calculus 1 class:

    Find the lim sin3t + 4t
    tsect

    when t approaches 0.

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  2. #2
    MHF Contributor
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    Quote Originally Posted by thaliaj_df View Post
    Find the lim sin3t + 4t
    tsect

    when t approaches 0.
    To learn how to format using only text, try here. My guess as to your meaning, using LaTeX formatting, is as follows:

    . . . . . \lim_{t \rightarrow 0}\, \frac{\sin(3t)\, +\, 4t}{t \sec(t)}

    A good way to start might be to split the addition into two parts, also converting the reciprocal of the secant into a cosine:

    . . . . . \lim_{t \rightarrow 0}\, \frac{\sin(3t)\, cos(t)}{t}\, +\, 4\cos(t)

    You learned an important trig limit, probably when you were learning trig derivatives:

    . . . . . \lim_{\theta \rightarrow 0}\, \frac{\sin(\theta)}{\theta}\, =\, 1

    With this in mind, restate the limit as:

    . . . . . \lim_{t \rightarrow 0}\, 3\left(\frac{\sin(3t)}{3t}\right) \cos(t)\, +\, \lim_{t \rightarrow 0}\, 4\cos(t)

    The cosine can be simply evaluated, and the sine fraction is the limit they gave you earlier.
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