Recent content by RPierre

Homework Statement Let L\in R and define h(x) = \begin{cases} sin(1/x) & \text{ if } x \neq 0 \\ L & \text{ if } x = 0 \end{cases} Prove that h is not continuous at 0 Homework Equations My Professor gave us the hint "Prove by contradiction, taking \epsilon...

Homework Statement This problem is insanely intuitive. Define f : (0,1) \rightarrow \Re by f(x)=\begin{cases} 1/q&\text{if } x \neq 0 \text{, is rational, and }x = p/q \text{in lowest terms}\\ 0&\text{otherwise }\end{cases} Suppose \epsilon > 0. Prove that there are at most a...

Homework Statement Prove that the limit as x->c of f(x) = L if and only if both one sided limits also = L Homework Equations Has to be an epsilon delta proof The Attempt at a Solution Being an if and only if, I have to do two cases : If A, then B. and if NOT A, then NOT B, logically...

**DISCLAIMER - I am super bad at LaTeX** Homework Statement Prove \lim_{x \rightarrow \infty}\frac{1}{1+x^2} = 0 Homework Equations I Think I proved it, but I feel like I'm missing something to make this a proof of ALL \epsilon>0 and not just one case. Maybe I did it right. I...

This is my first assignment ever with topological proofs, so bear with me. first, what is the map you defined , and why did you define it? Is that to say that any subset within S must also be open and closed? secondly, I've never encountered the idea of being "connected" before. I took the...

I'm not familiar with LaTex and assumed he wasn't using leibniz notation by the prime notation used and the level of calculus, so I simply whipped up a solution with simple principles. I'm sure the original poster got the point as the question was able to be resolved. Thanks for pointing that...

First, you must simplify your line for y = mx + b form. x + 2y - 6 = 0 -> x - 6 = -2y -> \frac{x-6}{-2} = y -> y = \frac{-1x}{2} + 3 Next, to find a line tangent to f(x), we take it's derivative f'(x) = 2x - 1 Compare the two slopes. 2 and -1/2. These are in fact...

I'll simplify this for you. See if you can solve the question from here: First, FOIL the numerator. Next, solve all of our components separately, so: h'(x) = \frac{d}{dx} (0.5t + 2)1/2 = \frac{1}{2}(0.5t +2)-1/2 * 0.5 <By Chain Rule> = \frac{1}{4}...

The main question: Let S be a subset in Rn which is both open and closed. If S is non-empty, prove that S= Rn. I am allowed to assume Rn is convex. Things I've considered and worked with: The compliment of Rn is an empty set which has no boundaries and therefore neither does Rn. Therefore...

Hey PhysicsForums, This is my first time here but I have seen many knowledgeable responses to tough questions and I truly am stumped. My question is as follows (This a third year Analysis course in my Mathematics undergrad degree): 1. Let A and B be Subsets of RN with Boundaries B(A) and...

Homework Statement I am new to this board, but I am at my wits end trying to solve this problem. If anyone could provide a somewhat detailed solution i would forever be in debt, thanks! One car, located at position (-29.9 , 0 ) is traveling at 12.7 m/s ( +x) Another Car, located at...