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Math Help - Evaluate this limit and explain why it cannot be determined.

  1. #1
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    Evaluate this limit and explain why it cannot be determined.

    a)

    b) Explain why the limit as x approaches 3 from the right cannot be determined.

    c) What can you conclude about


    For a I first tried to sub in 3 for x but that gives me the square root of 0 which is 0.. so is this indeterminite form?.. and i did it wrong?
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  2. #2
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    For your purposes, it is probably most effective to just graph the function f(x) = \sqrt{9-x^2} and notice what happens as you approach the point x=3 from the left and right sides.

    By the way, \sqrt{0} = 0 is perfectly valid. It's not an indeterminate form. However, it *is* a borderline case. i.e., if you went any smaller than 0, then a problem arises. This is definitely related to the problem.
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  3. #3
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    Quote Originally Posted by kmjt View Post
    a)

    b) Explain why the limit as x approaches 3 from the right cannot be determined.

    c) What can you conclude about


    For a I first tried to sub in 3 for x but that gives me the square root of 0 which is 0.. so is this indeterminite form?.. and i did it wrong?
    For part a)

    You are asked to determine

    \lim_{x \to 3^-}\sqrt{9 - x^2}.

    As said in a previous post, you should probably just graph the function and see what happens as x \to 3 from the left...


    For part b)

    Note that this function is only defined for 9 - x^2 \geq 0

    9 \geq x^2

    x^2 \leq 9

    |x| \leq 3

    -3 \leq x \leq 3.

    How can you make x approach 3 from the right if the function is not defined for any values of x to the right of 3?


    c) Limits only exist when the left hand limit and right hand limit are equal.

    Since there is a left hand limit but NOT a right hand limit, what does that tell you about the limit of this function?
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