Answer the following questions:
a)
b)
c)
Suppose a region A is easily described as the region between one curve on the left and another curve on the right. When computing thed would you integrate over X first, or over V first?
If R is a region in the plane, what geometric quantity does dA represent?
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Answer the following questions: a) b) c) Suppose fx,v) and g(x,y) are functions in the plane, and fx,y2gx, for all x and y in a region R. What geometric quantity does fx,y-g(x,y)dA represent? Suppo...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,1), (0 , 1). Find the area of the image of R in the ry plane? (b) Find the area of R by computing the Jacobian of the transformation from uv-space to xy-space Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice...
1 Let R be a region bounded between two curves on the r, y-plane. Suppose that you are asked to find the volume of the...
1 Let R be a region bounded between two curves on the r, y-plane. Suppose that you are asked to find the volume of the solid obtained by revolving the region R about the r-axis If you slice the region R into thin horizontal slices, i.e., parallel to the r-axis, in setting up the Riemann sum, then which method will come into play? A. Disc method B. Washer method C. Either disc or a washer method depending on the shape...
can younplease answer all of these i need it for a review please u-x+y, V--2x+y S...
can younplease answer all of these i need it for a review
please
u-x+y, V--2x+y S S 5ydx dy R where is the parallelogram bounded by the lines y=-x+1, y=-x +4, y = 2x + 2, y = 2x + 5 o Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral. The coordinate axes and the line § 35 dy dx x/3 5(1 - x/3) dy dx °? I ddy of...
1 Suppose V is the plane in R3 that contains the ponts a, b and g, where a (1,2,3), b-(1,-2,1) and c-(0,1,2) Suppose L...
1 Suppose V is the plane in R3 that contains the ponts a, b and g, where a (1,2,3), b-(1,-2,1) and c-(0,1,2) Suppose L is the lne in R3 that contains the pont a and is perpendicular to the plane V (a) Fınd an equation for V (b) Find an equation for L 2 Consıder the R2 - R function f defined by f (,y) (0,0) 2 (a) Write down the largest possıble doman Df of f (b) Prove from...
all a,b,c,d 1. Suppose C is simple closed curve in the plane given by the parametric equation and recall that the outward unit normal vector n to C is given by y(t r'(t) If g is a scalar field on...
all a,b,c,d
1. Suppose C is simple closed curve in the plane given by the parametric equation and recall that the outward unit normal vector n to C is given by y(t r'(t) If g is a scalar field on C with gradient Vg, we define the normal derivative Dng by and we define the Laplacian, V2g, of g by For this problem, assume D and C satisfy the hypotheses of Green's Theorem and the appropriate partial derivatives of f...
G-ly~2 _ cos(x + y2z)ļi + [xz2-2yz cos(x + y2z)| j + 12.ryz-v2 cos(x + y%)| k. (a) Which of these two fields (if any) are conservative on R? Give detailed (b) Find potential functions for the fields...
G-ly~2 _ cos(x + y2z)ļi + [xz2-2yz cos(x + y2z)| j + 12.ryz-v2 cos(x + y%)| k. (a) Which of these two fields (if any) are conservative on R? Give detailed (b) Find potential functions for the fields that are conservative. (c) Calculate the line integralsF - dr and / G dr where C is the arc of the reasoning 2 2 curve formed by the intersection of the plane 4 and the surface zy in the first octant, oriented...
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integra...
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integral dy dx into an integral over G, and evaluate both integrals
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then...
Consider 1-2 Vr? + y + 3 LLL da dydar. V1-38-98 V +y + y2 +22...
Consider 1-2 Vr? + y + 3 LLL da dydar. V1-38-98 V +y + y2 +22 +y +22-2 the origin to the point (2, y, ) makes with the z-axis is a new angle which we will label o, and we label the length of the line segment p. We can now determine the remaining side-lengths of our new triangle. Let us try to label our point (2, y, z) in only p and 6. Our labeled triangle gives us...
Suppose that the following equations govern planned spending in the US: C = 500 + 0.75(Y-T) T = 0.2Y – 800 I = 3000 – 64000r G = 3200 NX = 1000 – 10e (e =“trade weighted” real ex. rate. As always, inc...
Suppose that the following equations govern planned spending in the US: C = 500 + 0.75(Y-T) T = 0.2Y – 800 I = 3000 – 64000r G = 3200 NX = 1000 – 10e (e =“trade weighted” real ex. rate. As always, increase in e = $ appreciation) NFO = 500 – 60000(r – r FOR) r FOR = 3% a) Explain how NFO responds to an increase in the Home interest rate, and an increase r FOR, based on...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,1), (0 , 1). Find the area of the image of R in the ry plane? (b) Find the area of R by computing the Jacobian of the transformation from uv-space to xy-space Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice...
1 Let R be a region bounded between two curves on the r, y-plane. Suppose that you are asked to find the volume of the solid obtained by revolving the region R about the r-axis If you slice the region R into thin horizontal slices, i.e., parallel to the r-axis, in setting up the Riemann sum, then which method will come into play? A. Disc method B. Washer method C. Either disc or a washer method depending on the shape...
can younplease answer all of these i need it for a review
please
u-x+y, V--2x+y S S 5ydx dy R where is the parallelogram bounded by the lines y=-x+1, y=-x +4, y = 2x + 2, y = 2x + 5 o Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral. The coordinate axes and the line § 35 dy dx x/3 5(1 - x/3) dy dx °? I ddy of...
1 Suppose V is the plane in R3 that contains the ponts a, b and g, where a (1,2,3), b-(1,-2,1) and c-(0,1,2) Suppose L is the lne in R3 that contains the pont a and is perpendicular to the plane V (a) Fınd an equation for V (b) Find an equation for L 2 Consıder the R2 - R function f defined by f (,y) (0,0) 2 (a) Write down the largest possıble doman Df of f (b) Prove from...
all a,b,c,d
1. Suppose C is simple closed curve in the plane given by the parametric equation and recall that the outward unit normal vector n to C is given by y(t r'(t) If g is a scalar field on C with gradient Vg, we define the normal derivative Dng by and we define the Laplacian, V2g, of g by For this problem, assume D and C satisfy the hypotheses of Green's Theorem and the appropriate partial derivatives of f...
G-ly~2 _ cos(x + y2z)ļi + [xz2-2yz cos(x + y2z)| j + 12.ryz-v2 cos(x + y%)| k. (a) Which of these two fields (if any) are conservative on R? Give detailed (b) Find potential functions for the fields that are conservative. (c) Calculate the line integralsF - dr and / G dr where C is the arc of the reasoning 2 2 curve formed by the intersection of the plane 4 and the surface zy in the first octant, oriented...
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then usef(x.y) dx dy-f(g(u.v),h(u.v)|J(u,v)l du dv to transform the integral dy dx into an integral over G, and evaluate both integrals
a. Find the Jacobian of the transformation x = u, y = 4uv and sketch the region G: 1 s u s 2.4 s4uvs 8, in the uv-plane. b. Then...
Consider 1-2 Vr? + y + 3 LLL da dydar. V1-38-98 V +y + y2 +22 +y +22-2 the origin to the point (2, y, ) makes with the z-axis is a new angle which we will label o, and we label the length of the line segment p. We can now determine the remaining side-lengths of our new triangle. Let us try to label our point (2, y, z) in only p and 6. Our labeled triangle gives us...
13. Integrate: a. j«x+278)dx 0 b. (dx х c. dx 9+ x d . xdx? +2 dx 2x+1 хр '(x’+x+3) f. I sin (2x) dx g. cos (3x) dx h. ſ(cos(2x)+ + secº (x))dx i. [V2x+1 dx j. S x(x² + 1) dx k. | xe m. [sec? (10x) dx 16 n. .si dx 1+x 0. 16x 1 + x dx 5 P. STA dx 9. [sec xV1 + tan x dx 14. Given f(x)=5e* - 4 and f(0) =...
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