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Math Help - limit of a trig function

  1. #1
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    limit of a trig function

    Hi. I'm just a little confused about something.

    Here is the problem,

    limit as x approaches 0, of tan(pi/4(cos(sin x^(1/3))

    So it's simple, cube root of 0 is 0, and sin 0 is 0, cos of 0 is 1, and so pi/4*1=pi/4.

    So the limit is tan(pi/4), which is 1.

    They ask if the function is continuous at this point, x=0. According to my calculator, at x=0, f(x)=.999999999999999...

    I'm just not sure what this means. Does the point x=0, y=1 exist for this function?
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  2. #2
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    Re: limit of a trig function

    Quote Originally Posted by StudentMCCS View Post
    Here is the problem,

    limit as x approaches 0, of tan(pi/4(cos(sin x^(1/3))

    So it's simple, cube root of 0 is 0, and sin 0 is 0, cos of 0 is 1, and so pi/4*1=pi/4.

    So the limit is tan(pi/4), which is 1.

    They ask if the function is continuous at this point, x=0.
    Does f(0) exist?
    Does \lim _{x \to 0} f(x) = f(0)~?

    If you answer yes to both questions then f is continuous at x=0.
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  3. #3
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    Re: limit of a trig function

    Quote Originally Posted by Plato View Post
    Does f(0) exist?
    Does \lim _{x \to 0} f(x) = f(0)~?

    If you answer yes to both questions then f is continuous at x=0.
    According to my math, yes. But according to my calculator no. This is what I don't understand, why does the calculator say f(o)=.9999999, when it should say 1?
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  4. #4
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    Re: limit of a trig function

    Quote Originally Posted by StudentMCCS View Post
    According to my math, yes. But according to my calculator no. This is what I don't understand, why does the calculator say f(o)=.9999999, when it should say 1?
    Throw calculators away. They are useless for limits.
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  5. #5
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    Re: limit of a trig function

    Thanks Plato.
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