I can't follow the answer please explain.
7. (a) Consider the rectangle S in R3 with vertices (0,0,0), (1, 1,o), (a.1,2), and (0,0,2). Give...
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f: R3 → R be the function defined by f(x, y, z) = 1 - 2y + 32. Using the change of variables theorem, rewrite Ss f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral (8 points).
Consider the points u(1, 1,-1), v (a, 2,-1) and w (1,2,-1) in R3, where a e R. There are two possible values of a for which u, v and w will form an isosceles triangle. a) Find one of these values. (b) Determine the angle between the equal sides of the triangle. Consider the points u(1, 1,-1), v (a, 2,-1) and w (1,2,-1) in R3, where a e R. There are two possible values of a for which u, v...
Don't give the same solution. Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1,2,3), and (-1,0,1). Let f: R3 +R be the function defined by f(x, y, z) = 2 - 2y + 3z. Using the change of variables theorem, rewrite Js f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral
Let S CR be the tetrahedron having vertices (0,0,0), (0,1,1), (1, 2, 3), and (-1,0,1). Let f: R3 R be the function defined by f(x,y, x) = x - 2y + 3z. Using the change of variables theorem, rewrite Ssf as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral
6. Let S CR be the tetrahedron having vertices (0,0,0), (0, 1, 1), (1, 2, 3), and (-1,0,1). Let f:R3 → R be the function defined by f(x, y, x) = x – 2y + 3z. Using the change of variables theorem, rewrite Ss f as an integral over a 3-rectangle, then use Fubini's theorem to evaluate the integral (8 points).
Question 2 0 out of 4 points Let f(x,y) Xy be defined on the rectangle R [0,1]x [0, 1] and consider the partition of R given by P2RR1.2. R2.1, R2.21. where Rx Compute U(f,P2)-L(f,P2). Please give your answer in decimal form. 2 '2 Question 2 0 out of 4 points Let f(x,y) Xy be defined on the rectangle R [0,1]x [0, 1] and consider the partition of R given by P2RR1.2. R2.1, R2.21. where Rx Compute U(f,P2)-L(f,P2). Please give your...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
Consider the surface S, given by the parameterization: And consider the claims: S is smooth in all its points. S matches the graph of the equation Select one: a. Only (2) is true. b. Both are false. c. They are both true. d. Only (1) is true. r(u, v) = (u, v, u? + v2), donde Su<lyo Susi z2 = 2² + y para z>0yz² + y² <1.
1/3 x + y 7. Consider dA where R is the region bounded by the triangle with vertices (0,0), (2,0), V= x+y X-y and (0,-2). The change of variables u=- defines a transformation T(x,y)=(u,v) from the xy-plane 2 to the uv-plane. (a) (10 pts) Write S (in terms of u and v) using set- builder notation, where T:R→S. Use T to help you sketch S in the uv-plane by evaluating T at the vertices. - 1 a(u,v) (b) (4 pts)...
1 3. Consider the vector v= (-1) in R3. Let U = {w € R3 :w.v=0}, where w.v is the dot product. 2 (a) Prove that U is a subspace of R3. (b) Find a basis for U and compute its dimension. 4. Decide whether or not the following subsets of vector spaces are linearly independent. If they are, prove it. If they aren't, write one as a linear combination of the others. (a) The subset {0 0 0 of...