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Math Help - Need help with Calculus questions (Test Tommorow)

  1. #1
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    Need help with Calculus questions (Test Tommorow)

    Hey guys, I am having some difficulty with a couple of Calculus questions on my review. For the most part I feel pretty confident, but these four have been bothering me. (Also I can't types these symbols the way they are supposed to be.)

    1. lim as x approaches infinite (sqrt(x^2 - 9)) / 2x - 6

    (I am having trouble simplifying this equation to find the limit of f(x).)

    2. lim as x approaches 1 ((1/x-1) + (1/x^2-3x+2))

    (Same issue, having trouble simplifying this equation.)

    These last two are Intermediate Value Theorem questions.

    1. 2x^3 + x^2 + 2 = 0 (-2, -1)

    2. e^ -x^2 = x (0, 1)


    Any help or feedback would be appreciated, thanks.
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  2. #2
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    1. \lim_{x \to \infty} \frac{\sqrt{x^2-9}}{2x-6} = \lim_{x \to \infty} \frac{\sqrt{x-3}\sqrt{x+3}}{2(x-3)} = \lim_{x \to \infty} \frac{1}{2} \frac{\sqrt{x+3}}{\sqrt{x-3}} = \lim_{x \to \infty} \frac{1}{2} \sqrt{\frac{x+3}{x-3}} = 1/2
    2. \lim_{x \to 1} \frac{1}{x-1} + \frac{1}{x^2-3x+2} = \lim_{x \to 1} \frac{1}{x-1} + \frac{1}{(x-1)(x-2)} = \lim_{x \to 1} \frac{x-1}{(x-1)(x-2)} = -1

    I'm afraid I don't know what the rest of the questions are asking. Good luck!
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  3. #3
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    Thanks for the feedback, I was actually on the right track on figuring those two problems out, but screwed up a bit in the end. Appreciate it.

    Does anyone know how to solve those intermediate value theorem questions?
    I am still a bit confused on how to solve them.
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  4. #4
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    Quote Originally Posted by Gitano View Post
    Thanks for the feedback, I was actually on the right track on figuring those two problems out, but screwed up a bit in the end. Appreciate it.

    Does anyone know how to solve those intermediate value theorem questions?

    These last two are Intermediate Value Theorem questions.

    1. 2x^3 + x^2 + 2 = 0 (-2, -1)

    2. e^ -x^2 = x (0, 1)

    I am still a bit confused on how to solve them.
    You have given two equations. What is the actual question? What is meant to be done with these equations?
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