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Thread: Continuity lim x->-13*pi/14 cos(7x - cox(7x))

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    Continuity lim x->-13*pi/14 cos(7x - cox(7x))

    Help please
    I should be able to just apply x into the function but I'm having trouble solving

    lim x->-13*pi/14 cos(7x-cox(7x))

    I get to

    cos(-13*pi/2 - cos(-13*pi/2))

    what next?

    Thanks
    Last edited by muzik; 02-02-2018 at 05:15 PM.

  2. #2
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by muzik View Post
    I should be able to just apply x into the function but I'm having trouble solving

    lim x->-13*pi/14 cos(7x-cox(7x))
    Would it be correct to interpret the above as follows?

    . . . . .[tex]\displaystyle \lim_{x \rightarrow -\frac{13\pi}{14}}\, \cos\left(7x\, -\, \cos(7x)\right)[/tex]

    Quote Originally Posted by muzik View Post
    I get to

    lim x->-13*pi/14 cox(-13*pi/7 - cos(-13*pi/7))

    what next?
    Is there any reason you can't just plug-n-chug in your calculator?

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    Quote Originally Posted by muzik View Post
    Help please
    I should be able to just apply x into the function but I'm having trouble solving

    lim x->-13*pi/14 cos(7x-cox(7x))

    I get to

    lim x->-13*pi/14 cox(-13*pi/7 - cos(-13*pi/7))
    Yes, since the cosine is continuous (and I assume you meant cos everywhere, not cox), you just have to find the value of cos(7x - cos(7x)) when x = -13*pi/14. But that is not what you did. Is that just more typos, or is the problem something other than what you wrote? You don't seem to have multiplied by 7 in either place. You should have

    cos(7(-13*pi/14) - cos(7(-13*pi/14)))

    Once you do the right substitution, just use a calculator to do what you wrote!

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    Thanks for the replies and sorry for the typos
    Stapel, Yes that's correct interpretation.

    ok if I enter into calculator I get 0.8414.

    It's my last attempt on the answer for the problem. Does 0.8414 sound right?
    The requirement is to "Simplify your answer" Usually it will say up to 4 decimal places.

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    Quote Originally Posted by Dr.Peterson View Post
    Yes, since the cosine is continuous (and I assume you meant cos everywhere, not cox), you just have to find the value of cos(7x - cos(7x)) when x = -13*pi/14. But that is not what you did. Is that just more typos, or is the problem something other than what you wrote? You don't seem to have multiplied by 7 in either place. You should have

    cos(7(-13*pi/14) - cos(7(-13*pi/14)))

    Once you do the right substitution, just use a calculator to do what you wrote!
    I was trying to simplify. The 7 with the denominator 14. so with out the cosine I was trying to simplify 7(-13*pi/14) so I that's how I got -13*pi/2. oops and I wrote -13*pi/7 in my earlier post.

    I'm just thinking the answer is not in decimal form.

    Thanks for your help.

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    Quote Originally Posted by muzik View Post
    I was trying to simplify. The 7 with the denominator 14. so with out the cosine I was trying to simplify 7(-13*pi/14) so I that's how I got -13*pi/2. oops and I wrote -13*pi/7 in my earlier post.

    I'm just thinking the answer is not in decimal form.
    I would expect the answer to be a decimal - trig functions are rarely rational.

    What answer do you get? Show us that, and the specific calculation you really do to get it.

    And, as you've learned, be sure to proofread before you hit Submit!

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    Quote Originally Posted by Dr.Peterson View Post
    I would expect the answer to be a decimal - trig functions are rarely rational.

    What answer do you get? Show us that, and the specific calculation you really do to get it.

    And, as you've learned, be sure to proofread before you hit Submit!
    I take back what I said! Do the simplification correctly, and evaluate by hand as far as you can. What is the value of the cosine of -13*pi/2? Think about it!

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    So i'm down to

    cos((-pi/2)-cos(-pi/2)) correct?
    =cos((-pi/2)-0)
    =cos(0-0)
    =cos (0)
    =1

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    Quote Originally Posted by Dr.Peterson View Post
    I take back what I said! Do the simplification correctly, and evaluate by hand as far as you can. What is the value of the cosine of -13*pi/2? Think about it!
    cos(-pi/2) ?

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    Quote Originally Posted by muzik View Post
    cos(-pi/2) ?
    Hint:

    cos(π/2) = 0
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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