Thread: Need help with Calculus questions (Test Tommorow)

1. 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.

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!

2. 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.

3. Originally Posted by Gitano
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?