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...
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...