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Math Help - What are the LIMITS of these functions?

  1. #1
    ADH
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    Cool What are the LIMITS of these functions?



    What is the limit of sin(x) as x is approaching infinity?

    Also, what is the limit of tan(x) when x is approaching pi from the right? (RIGHT HAND LIMIT)

    Last, what is the limit of tan(x) when x is approaching to pi?

    And last one, what is the limit of f(x) (4/x , x less than 1) and (x^3 - 2x + 5 , x greater than 1.) This function is probably peicewise.

    Thank you very much.

    Thank you!
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  2. #2
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    \lim_{x \to \infty}\sin{x} does not exist, because the function continues to oscillate around [-1, 1].


    \lim_{x \to \pi}\tan{x} = \lim_{x \to \pi}\frac{\sin{x}}{\cos{x}}


    =\frac{\sin{\pi}}{\cos{\pi}}

    =\frac{0}{1}

    =0.

    This is the same coming from the right and the left.


    Your final question is unreadable...

    Are you asking what is

    \lim_{x \to 1}f(x) where f(x) = \begin{cases}\frac{4}{x} \textrm{ if }x<1\\ x^3 - 2x + 5\textrm{ if }x>1\end{cases}?
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  3. #3
    ADH
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    Thank you. Except for my last question, it's 4/x, not 4x.
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  4. #4
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    To evaluate that limit, if it exists, work out what the function approaches from the left (when x < 1) and what the function approaches from the right (when x >1. If they are the same, then the limit exists and is this value.
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