Recent content by _Steve_

Oh, okay, so how do I get a g(t) with only one function from 0<t<2 instead of having: g(t)={f(t), t<1 h(t), t>1) ? Does it make sense to write: G(t)={0, t<0 F(t), t<1 H(t), t>1 1, t>2} as: G(t)={0, t<0 F(t)+H(t), 0<t<2 1, t>2} ? EDIT: Nevermind, I think I was doing the other part of the...

Hey guys, I'm stuck on a question in my homework assignment and I was wondering if you could push me in the right direction? So here's the question: X and Y are continuous random variables with joint pdf f(x,y)= 4xy (0<x<1, 0<y<1, and otherwise 0). Find the pdf of T=X+Y using the CDF...

Ohh, I see what you're saying, when y=-x, the denominator of fx = 0, so would I just say that f(x,y) isn't differentiable when y=-x? Or do I have to go back to limits and use squeeze theorem somehow? (Just a cause cause the hint looks like squeeze theorem :P)

So I'm not done the question? What am I looking for at the moment to show that it's differentiable? Sorry, just trying to understand the question better! :)

Hey guys, I'm just wondering if I got this question right: Discuss where the following in R^{2} is differentiable: f(x,y)=(x^{3}+y^{3})^{2/3} So I take the partial derivative: f_{x}(x,y)=\frac{2x^{2}}{(x^{3}+y^{3})^{1/3}} and see that f(x,y) might not be differentiable at (0,0), so...

Ok! I get it now, thanks a lot for all the help! I'm starting to dread integration of multivariable functions now though :P

Hahaha atm/at the moment, same thing! (god wouldn't that be terrifying!) Ok! I think I understand. I'm just trying to see where you CAN plug in numbers for... For 1) you can plug in any x,y and get an answer For 2) any x, y works, even though there's no y, it just means it works for any y For...

Hey guys, I'm doing some multivariable calculus atm, and I need some help with the Domains of some multivariable functions... 1) f(x,y) = 3x^2 + 2y The problem I'm having here is I basically forget the definition of domain... would it be for all x and y even though there are two whole quadrants...

I figured it out, decided to post the answer just in case someone else has the same kind of question sometime... basically just change the numerator to: (|x|^c)^(a/c) (|y|^d)^(b/d) and use the inequalities: |x|^c <= |x|^c + |y|^d |y|^d <= |x|^c + |y|^d then cancel out and use squeeze theorem

It's the second one. I tried to put the vector lines over the x and 0 lol. Yeah I'm not sure how to start this! Should I try using Squeeze theorem with something? Or the definition of a limit?

Show that if a, b \geq 0 and c, d > 0, with \frac{a}{c} + \frac{b}{d} > 1, then: lim_{\vec{x}\rightarrow\vec{0}} \frac{|x|^{a}|y|^{b}}{|x|^{c}+|y|^{d}} = 0 Sorry guys, totally forgot about latex! Here's a more readable version...

I need to show that limit (|x|^a*|y|^b) / (|x|^c+|y|^d) = 0 (x,y)->(0,0) when a,b>=0; c,d>0; with a/c + b/d > 1 Does anyone have some tips for starting off the proof?

So the function I'm working with is: f(x,y) = 1/sqrt(1-x^2-4y^2) First, they want me to find the Domain and Range, which I found to be: D: x^2 + 4y^2 < 1 R: (0,1] Then they want me to sketch level curves and cross sections, then sketch f(x,y) I'm having trouble with the sketching, I...

I figured them out! Thanks Mark! Is a lower bound really necessary? I assumed not, because it will obviously be larger than x_{1}=0 since the sequence is increasing

I've got two calculus proofs that I can't seem to get! I was wondering if you guys could help me out a bit... 1. Homework Statement Suppose x_{n} is the sequence defined recursively by x_{1}=0 and x_{n+1}=\sqrt{5 + 2x_{n}} for n=0, 1, 2, 3, ... Prove that x_{n} converges and find...