http://www.math.rutgers.edu/~greenfie/webstuff/pdfstuff/w6W.pdf
is the problem
For the first part, I believe it is just tracing, right? I look at the line at (0,1) and then follow it, but it's a little confusing.
Next
It says how many critical points...well a critical point is when it is...
Well, then for the complement, there is a neighborhood (x-eps,x+eps) that is contained in T since there are infinitely many points on our domain such that h(x)=/=0 because of the fact that h is continuous.
Thanks
Hmm...okay...so an open set is one where if x belongs to the set T, then there is a neighborhood Q of x that is contained in the set T.
So if T={x: f(x)=/=g(x)}, then we can find a neighborhood of x of T , namely (x-eps,x+eps) that is contained in T. Well...obviously if the function...
Suppose f:[a,b]--> R and g:[a,b]-->R. Let T={x:f(x)=g(x)}
Prove that T is closed.
I know that a closed set is one which contains all of its accumulation points. I know that f and g must be uniformly continuous since they have compact domains, that is, closed and bounded domains. Now T is the...
Well, then can I say to assume that because I am trying to do a proof by contradiction.
I'm confused by what you are saying...I should say A=B=C=D=R and then what? I'm not sure I follow...is the rest okay?
Homework Statement
A,B,C,D are sets.
Prove that if C is contained in A and D is contained in B, then C∩ D is contained in A∩ B.
Homework Equations
The Attempt at a Solution
Let x be any element.
Then There exists (x that belongs to C∩D) and (x does not belong to A∩ B)
So...
I got it since the volume of a cone is (1/3)* pi* r^2* h and since we are looking at a cone in this problem and we need to integrate the volum*density*g.
Ok great...thank you very much for your help.
The one last thing is...so we don't include the 1/3? That's because we already used it when finding r(h), correct? (just want to be completely sure).
Ok so I see it as a line...We have pts. (0, sqrt 27) and (10,0) so the slope is:
-sqrt(27)/10
And so
r(h)= -sqrt(27)/10*h + sqrt(27)
And I suppose the other cone would be found in a similar manner...just the points would be (10,sqrt 27) and (0,0)
Is that correct? And if so, I'm...
I will take g=10 for simplification purposes.
For the cylinder, we have it as
integral (0 to 10) 270000* pi* h dh=
13500000* pi J
Now we look at the inverted cone and we have integral(0 to 10) 30000 * pi * r^2 * h dh
But my problem is, how do I find what r is for the cone?
Do I...
Homework Statement
http://www.math.rutgers.edu/~greenfie/mill_courses/math152/pdfstuff/w2.pdf
problem 2
Homework Equations
Work is the integral of force..
The Attempt at a Solution
Problem 2:
Basically I know how to calculate the work for the cylinder. Since they have...