3. Let || P| be the norm of the partition or the length of the longest diagonal of the Dr. A sum of the form Σ-1 F(x, y, z) AV, where (x, y, z) is an arbitrary point within each D and AV denotes the volume of each D, is called a Riemann sum. The type of partition used in step 2, where all the D, lie completely within D, is called an inner partition of D.

Q: Let (X, dx) and (Y, dy) be metric spaces, and let A and B be disjoint closed subsets of X X Y. Show…

A: Given:Metric spaces  and Disjoint closed subsets  and Objective: To show that there exists a…

Q: Let g be bounded on [a, b] and assume there exists a partition P with L(g,P) = U(g,P). Describe g.…

A:

Q: 2. Can you make a conformal map that maps the region bounded by |z + 1| = 1 and |z| = 2 to the…

A: Given: |z+1|=1 |z|=2

Q: = Consider two metric spaces (X, dx) and (Y, dy). The cartesian product Z X X Y becomes a metric…

A:

Q: Let P, be an equidistant partition of [2, 4] on f(x) = x , then U(f, P,) =

A: To find the U(f, pn) of the function f(x) = x

Q: Determine where D is the region enclosed (5, 0, 0), (0,3,0), (0, 0, 3), by the tetrahedron with…

A:

Q: Let X =ela, b), spoce of all continuous function defined on fa, b] Find diameter of X , dia (X) =…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let E be the volume described by 0sxsa , 0sysb, 0szsc, and F= x²i + y²j + z?k. Compute F. NdS Select…

A: Given F=x2i+y2j+z2k to find  ∫∫∂EF.Ndswhere E is th evolume described by0≤x≤a,0≤y≤b,0≤z≤c

Q: Let X = ca, b], space of all continuous function de f ined on a, b] %3D Find diameter of X, dia (X)…

A: Diameter of a function space

Q: Let I = , zdV ,where D is bounded by the planes x = 0, z = 0, x+ y = 2 and the cylinder x2 + z2 = 1…

A:

Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

A:

Q: If f : [a, b] → R and P be a partition of a, b . Then f is Riemann integrable if and only if its…

A:

Q: 8. Let a, b, c > 0. Find the volume of the region bounded by the coordinate planes and the surface…

A:

Q: Let G = (x, y | x* = y* = e, xyxy = e). Show that IG| < 16. As- suming that |GI = 16, find the…

A: Given,                           G=x, y| x4=y4=e, xyxy-1=e, &amp;  G=16. To prove that G≤16. To find…

Q: Let g: [a, b] → R be a bounded function, and suppose that there exists a partition P so that L(g, P)…

A:

Q: = 1 be a partition Theorem 5.5. Let 0 = 0 < x1 < x2 <...<M <IM+1 of [0, 1] and h(x) = (xj+1-xj), x =…

A:

Q: let x be a discrete space and let a be subset of x find int(a) and ext(a) and boundary if (a).

A: We know the definition of discrete topology ,  The largest topology contains all subsets as open…

Q: A partition P = {I0, I1, I2,...,In 1,Tn} of the interval [a, b) is said to be "regular" if the…

A:

Q: Let f be a bounded Riemann integrable function on [a, b] and let P be a partition of [a, b]. Then…

A: Given that f is bounded Riemann integrable function on [a,b] and P be a partition of [a,b]. The…

Q: Let Y be any topological space and y: [0, 1] → Y be a continuous function so that r(0) = r(1) = xp.…

A:

Q: 1. Find the volume of the region in the first octant bounded by the coordinate planes 2 and the…

A: To find : Volume of the region in the first octant bounded by the coordinate planes and the surface…

Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A (A)° = A - int A %3D…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1) Prove that for any space, X, with any topology, T, that: (i) CI(X) = X and (ii) Int(X) = X.

A:

Q: Compute Lpf) and Up(f) for the function f(x) = x2 defined on 1= [0,1] where p is the partition…

A: Given that  f(x)=x^2 [0,1] n=5 subintervals

Q: Prove: f € R(a) if and only if for each ɛ > 0, there exists a partition of [a, b ] , say go, such…

A: f∈Rα if and only if for each ε&gt;0,there exists a partition of a, b,say P, such that UP, f, α-LP,…

Q: Let Y be any topological space and y: [0,1] → Y be a continuous function so that y(0) = r(1) Show…

A: