hi, I just thought I should point out that your upper riemann sum is less than your lower riemann sum.
I'm sure you're well aware that for any parition P, we have that Spf >= spf.
I suggest redrawing your graph making sure that you have chosen the appropriate height/width for the...
Homework Statement
if H is a normal subgroup of G and has index n, show that g^n is in H for all g in G.
The Attempt at a Solution
Take H a normal subgroup of a group G. Take g in G.
Consider gH in the quotient group G/H. Because |G/H| = [G:H] = n, (gH)^n = eH.
But g^nH =...
Homework Statement
the kneser graph KG(n:k) is the graph whose vertices are all of the k-subsets of {1,2,...,n} with 2 vertices beign adjacent if they are disjoint.
show KG(n:k) is vertex transitive
Homework Equations
a graph G is vertex transitive if for any 2 vertices x,y in G...
Homework Statement
Change the order of integration in the following double integral
integral from o to a, integral from 0 to sqrt(2ay-y^2) f(x y) dx dy
so i can see its a semi circle with center at (0,a)
x= sqrt(2ay-y^2) can be expanded by squaring both sides. then completing...
Homework Statement
let L(x)= integral from 1 to x: 1/t dt. Show that L:]0,infinity[--->R is continuously differentiable. show that L(xy)=L(x)+L(y) for all x,y in ]0,infinity[.
hint: let L1(x)=L(xy) and compute L'1(x)
you don't have to solve it for me, just lead me in the right...
Homework Statement
the integral from 0 to 1 given:
1 / [ (x^1/3)(x^2+2x)^1/2 ] dx
please explain,, thank you!
The Attempt at a Solution
At 0 the integrand behaves as 1/x^1/3*x^1/2 = 1/x^1/6 which is convergent as the exponent is <1
The Attempt at a Solution
It suffices to show that f^2 is integrable, since
fg= [(f+g)^2-(f-g)^2]/4
The function x --> x^2 is uniformly continuous on the range of f,
im not sure how to turn this into a formal proof, I am lost
Riemann integration
Homework Statement
set up an integral in cylindrical coords to compute the volume of the solid S bounded by the sphere x^2+y^2+z^2=12 and the cone 3z^2=x^2+y^2 where z>=0
The Attempt at a Solution
i will post my answer here. please let 'I' stand for integral:
i get,
I[0,2pi]...
Homework Statement
change the order of integration in the follwing double integral:
intgral [0,a] integral [0,sqrt(2ay-y^2)] f(x,y) dx dy
if x= sqrt(2ay-y^2),, do i solve for y or something,,ive used the computer to graph it but that didnt help me.