I need full solution of this with good explanation of each
answer
Homework Answers
when we did dx dy we get -0.5
and with dy dx 0.5
one is negative of other
for any doubt
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Use WolframAlpba to compute each of the double integrals below. Do your results contradict the Fu...
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not d...
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem)
Question 2...
1. (6 pts each) Compute the following line integrals. Sketch the path of integration and indicate...
1. (6 pts each) Compute the following line integrals. Sketch the path of integration and indicate the direction of positive orientation. (a) (xy2+ z2ds where C is the curve r(t)- (2sint, t,2 cost), O s t s 2TT/3. (b) F dr where F(x,y)(x + y,x -y) and C is the ellipse
1. (6 pts each) Compute the following line integrals. Sketch the path of integration and indicate the direction of positive orientation. (a) (xy2+ z2ds where C is the curve...
PLEASE ANSWER BOTH AND SHOW WORK FOR A RATING. THANK YOU! 15.2 Double integrals over general...
PLEASE ANSWER BOTH AND SHOW WORK FOR A RATING. THANK YOU!
15.2 Double integrals over general regions: Problem 1 Previous Problem Problem List Next Problem (1 point) Calculate the Riemann sum for f(x, y) = 7x – 2y and domain D in Figure 2 with two choices of sample points, and o. Which do you think is a better approximation to the integral of fover D? Why? y 4 O o o 3 o 2 1 O 0 1 2...
Double Integration Rerated integrals Example We evaluate the iterated integrat To evaluate the integral synbolically, we can proceed in two stapes syss x y Use MATLAB to evaluate the double inte...
Double Integration Rerated integrals Example We evaluate the iterated integrat To evaluate the integral synbolically, we can proceed in two stapes syss x y Use MATLAB to evaluate the double integrat using the method defines in the above exanple: 2) 2) C Reset ㎜ MATLAB Dannin ia save Your Script Question1 11y 、Question 2 12.y "、Question 3
Double Integration Rerated integrals Example We evaluate the iterated integrat To evaluate the integral synbolically, we can proceed in two stapes syss x...
Use double integrals to licate the fentroid of a two-dimensional region. LOOK AT ALL OTHER PHOTOS...
Use
double integrals to licate the fentroid of a two-dimensional
region. LOOK AT ALL OTHER PHOTOS AS EXAMPLES AND STEPS ARE INCLUDED
WITHIN!!!
Use double integrals to locate the centrold of a two-dimensional region Question Find the centroid (Ic, yc) of the trapezoidal region R determined by the lines y = -x + 2 y = 0y = 4,2= 12, and =0 Provide your answer below: FEEDBACK MORE INSTRUCTION SUBMIT Content attribution Question Calculate the component of the centroid with...
Consider the following region and the vector field F. a. Compute the two-dimensional divergence of the...
Consider the following region and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency F= (2x-2y); R=(x,y): x2 + y²59 a. The two-dimensional divergence is (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates with r as the radius and O as the angle SO rdr d0 (Type exact answers.) 0 o Set up the line...
Use double integrals to calculate the area, total mass, the moments about each axis, and the cent...
Use double integrals to calculate the area, total mass, the
moments about each axis, and the center of mass of the region. Plot
the location of the center of mass on the region.
2, R is the shaded region in Fig.6 and δ(r, e)-r y-sin(30) 04 0.2 05 Fig. 6 19
2, R is the shaded region in Fig.6 and δ(r, e)-r y-sin(30) 04 0.2 05 Fig. 6 19
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Com...
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F
3. Consider the...
Consider the following region R and the vector field F. a. Compute the two-dimensional curl of...
Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (3y, - 3x); R is the triangle with vertices (0,0), (1,0), and (0,2). . a. The two-dimensional curl is (Type an exact answer.) b. Set up the integral over the region R. JO dy dx 0 0 (Type exact answers.) Set up the line integral for the line...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vec...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem)
Question 2...
1. (6 pts each) Compute the following line integrals. Sketch the path of integration and indicate the direction of positive orientation. (a) (xy2+ z2ds where C is the curve r(t)- (2sint, t,2 cost), O s t s 2TT/3. (b) F dr where F(x,y)(x + y,x -y) and C is the ellipse
1. (6 pts each) Compute the following line integrals. Sketch the path of integration and indicate the direction of positive orientation. (a) (xy2+ z2ds where C is the curve...
PLEASE ANSWER BOTH AND SHOW WORK FOR A RATING. THANK YOU!
15.2 Double integrals over general regions: Problem 1 Previous Problem Problem List Next Problem (1 point) Calculate the Riemann sum for f(x, y) = 7x – 2y and domain D in Figure 2 with two choices of sample points, and o. Which do you think is a better approximation to the integral of fover D? Why? y 4 O o o 3 o 2 1 O 0 1 2...
Double Integration Rerated integrals Example We evaluate the iterated integrat To evaluate the integral synbolically, we can proceed in two stapes syss x y Use MATLAB to evaluate the double integrat using the method defines in the above exanple: 2) 2) C Reset ㎜ MATLAB Dannin ia save Your Script Question1 11y 、Question 2 12.y "、Question 3
Double Integration Rerated integrals Example We evaluate the iterated integrat To evaluate the integral synbolically, we can proceed in two stapes syss x...
Use
double integrals to licate the fentroid of a two-dimensional
region. LOOK AT ALL OTHER PHOTOS AS EXAMPLES AND STEPS ARE INCLUDED
WITHIN!!!
Use double integrals to locate the centrold of a two-dimensional region Question Find the centroid (Ic, yc) of the trapezoidal region R determined by the lines y = -x + 2 y = 0y = 4,2= 12, and =0 Provide your answer below: FEEDBACK MORE INSTRUCTION SUBMIT Content attribution Question Calculate the component of the centroid with...
Consider the following region and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency F= (2x-2y); R=(x,y): x2 + y²59 a. The two-dimensional divergence is (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates with r as the radius and O as the angle SO rdr d0 (Type exact answers.) 0 o Set up the line...
Use double integrals to calculate the area, total mass, the
moments about each axis, and the center of mass of the region. Plot
the location of the center of mass on the region.
2, R is the shaded region in Fig.6 and δ(r, e)-r y-sin(30) 04 0.2 05 Fig. 6 19
2, R is the shaded region in Fig.6 and δ(r, e)-r y-sin(30) 04 0.2 05 Fig. 6 19
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F
3. Consider the...
Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (3y, - 3x); R is the triangle with vertices (0,0), (1,0), and (0,2). . a. The two-dimensional curl is (Type an exact answer.) b. Set up the integral over the region R. JO dy dx 0 0 (Type exact answers.) Set up the line integral for the line...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...
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