f(x, y, z) . The total differentia %3D by o af Aæ + af Ay + az fe -Az df o df df · Ay + dz Az Ax + dx dy

Q: y y = f(x) Area -0.6 Areа%3D1.4 a c d Area =2.7 (a) ) dx = i (b) r) dx = i (c) ) ix = i (d) (x) dx =…

A: We have to find area

Q: solive dk d t.bounded.bg..Xy=16..

A: 1st we will draw region bounded by given curve in  1st quadrant . and then will find limit for…

Q: $5y dx + 4x dy,where C is the square with vertices (0, 0), (2, 0). (2, 2), and (0, 2) oriented…

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Q: 3) y' dx-(xy+y*) dy-o Let the substitution v= i y vx; dy-vdx+xdv %3D )x*dy+(2xyy*) ax -o Let the…

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Q: Verilen diferansiyel denklemin genel çözüm fonksiyonu aşağıdakilerden hangisidir? d?y dy -3x + 3y :…

A: Solving the  given differential equation

Q: Evaluate |[[p(4z + 3y² + 2x)dV = {(x, y, z) | 0<x < 2,0 sys 2, 0 s z < 1} .

A: We have to evaluate the triple integral given below: ∭B4z3+3y2+2xdV  Here, the region B in three…

Q: Evaluate 3xz dV where E = {(x, y, z) | 1 < æ < 3, x < y < 2æ, 0 < z < x + 3y}

A: ∬∫Ef(x,y,z) dV = ∫x=ex=f∫y=cy=d∫z=az=b f(x,y,z)dzdydx                                where , E…

Q: Evaluate e |/| 2xz dV where E = {(x, y, z) | 0 < z < 1, ¤ < y < 2x, 0 < z < z + 3y} E Round your…

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Q: 3x sec (xy)dA; R={{x,y): 0 sxs7,0 sys 1}

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Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2 - 7x, x= 6, Ax = 0.5 %3D %3D dy =…

A: Given y=x2-7x, x=6, dx=∆x ⇒dy=dydx·dx and ∆y=y(x+∆x)-y(x)

Q: i $ 6x³e**+3 dx. Using integration by parts (S udv = uv – f vdu) and letting u = f(x), dv = 3g(x)dx,…

A: Using integration by parts

Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2 - 5x, x = 4, Ax = 0.5 Ay = Ду %3D dy…

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Q: dx If z4 = x+y2, dy 3, and z > 0, find dz -1, dt at (x, y) = (0, 4). dt %3D %3D dt Please give an…

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Q: z = x* + xy", x = uv* + w², y= u +ve" dz when u = dv Find 3, v = 1, w = 0

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Q: Evaluate 3xz dV where E E = {(x, y, z) | 1 < x < 2, x < y < 2x, 0 < z < x + 3y} %3D

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Q: 3xz dV where E: {(x, y, z) | 0 < r < 2, x < y < 2x, 0 < z < x + 3y} Evaluate E

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Q: D eter mine Paricular volution ( 2xy)dy = (y²-x²)dy j x=I,y= -2

A: In this question we have to determine the particular solution.

Q: ( b) SI[ vzcos(x* µV where E = {(x, y, z) |0 < x < 1, 0 s y s.x, x S z 5 2x } E

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Q: Ⓒ Given SS² +8 dy dx. Reverse the order of in tegration and evaluate. Draw the region.

A: In the given problem first we draw the region then reverse the order of integration and after that…

Q: dy Find given that dt dx x + y = 2x + 4y, x= 3 y = 1, and %3D = 6 dt dy %3D dt

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Q: sta lis ūcally independent RVs x&y have pdfs fe (x) = 3 (4-x2), - 2<x<2 %3D 32 ノ fy (4) = ニ 1, Find…

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Q: find the indicated extrema, assuming that x, y, and z ar = xyz z - 12 = 0

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Q: dy If ex+У%3D ху, then dx %3D Ух- 1) A x(у- 1) (1- x) B x(y- 1) x(у- 1) Ух- 1) x(1-у) (D y(x- 1)

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Q: Compute (a) Ay and (b) dy for the given values of z and dx = Az. y = 4/x, I = 1, Ax = 1 (a) Ay = (b)…

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Q: |0 (x, y, z) | dV dz dr de |0 (z, r, 0)

A: In cylindrical coordinates

Q: IL Evaluate (x + y – 3z) dV where E = {(x, y, z) | - 7< y< 0,0 < a < y, 0 < z < x + y?}

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Q: /// 2xz dV where = {(x, y, z) | 1 < x < 4, x < y < 2æ, 0 < z < x + 3y} Evaluate E E %3D

A: We are asked to evaluate the integral.

Q: dy +y When reduced to a linear DE of order one in z, the Bernoulli's equation |=3x?y? becomes dz (A…

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Q: f (x, y) = xlx - alny is %3D O homogeneous 0 degree O not homogeneous O homogeneous 2nd degree O…

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Q: Let v=y" BERNOULLI'S EQUATION: dv = (1-m) y'm-'- (1-) y-n dy |-n-| dy + PCx)y - Q67)y^ %3D v dv =…

A: Bernoulli's Equation is of the form dydx+p(x) y = q(x) yn we will solve the Bernoulli's problem…

Q: Transform xydy = y? dx + ydy into a separation variable form. O (x – 1) dæ ydy = 0 - - de dy %3D a-1…

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Q: y(2x^2-xy+y^2)dx - x^2(2x-y)dy = 0 when x=1 ; y=1/2 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y)…

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Q: [xcsc (y/x) - y]dx + xdy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A: The given differential equation is; [xcsc (y/x) - y]dx + xdy = 0

Q: dy y(x-y) dx x(x+ y) The separable form of by taking y= vx and dy dv -=v+x is : dx dx Select one: a.…

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Q: Using the substitution *=vy, dx=vdy + ydv , the DE (1+2e*y) dx +2e*/» ( 1 – –) dy=0 reduce %3D (A…

A: We have to choose the correct answer from the given option according to the given condition

Q: dy using the given information. Calculate dt dx xy +x = 12; dt =-3, x= 2, y= 5 %3D O A. 3 О В. -9…

A: The equation is given by xy+x = 12 ; dxdt =-3, x = 2,y= 5 To evaluate : The value of dydt

Q: Compute Ay and dy for the given values of x and dx = Ax. %3D y = x2 - 5x, x = 4, Ax = 0.5 Ay = dy =…

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Q: The joint PDF of X and Y is 5y -1< x< 1, x² < y<1 fx,y(x, y) = 4 otherwise, %3D Find E(VY).

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Q: First order linear in (y-x+xycotx)dx+xdy=0

A: The given problem is to find the solution for the given first order linear differential equation.…

Q: II (2x + 3y + 4:") dV , where B = {(x, y, 2) | 0 < x < 1, 0 <y< 2, 0< 2< 3}

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Q: 4) answer: Check for Linear Independence 2x fi - e e; f2= i fs e* Say sa'y dx" 4 dy dx dx get the…

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Q: e-(z²+y²+z²) dV. x² + y² + z² where E is the region bounded by the spheres x? + y² + z² 1 and x? +…

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Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2 - 4x, x = 3, Ax = 0.5 Ay dy

A: Explanation of the answer is as follows

Q: dy The D.E. y? – a? can be classified as %3D da x²y (A) First-order linear (B) Separable (C)…

A: The given differential equation is                                                  dydx=y2-x2x2y…

Q: : // (x + y – 32) dV where E = {(x, y, z) | 0 < y < 1, 0 < x < y, 0 < z < r + y³} Evaluate - E

A: Triple integration

Q: condition a) dy - Va,y(4) -0 %3D dx b) dx dy -xVx +9,y(-4) =0 dy c) dx x +1 10 y(0) = 0 %3D

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Q: (x-2y) dx + (2x+y)dy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

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Q: dy x2 + y2 if dx Find at (x, y) = (5, 6) and z? dz dt = 9 and = 7. dt dt dz dt Additional Materials

A: To determine the derivative.

Q: dy The D.E. y2 – a? - can be classified as %3D dæ (A) First-order linear (B) Separable (C)…

A: We break this into simplier form then identify it's property.

Q: 2. Compute and x² - y² (x² + y²)2dX(y)dX(x) [0,1] [0,1] 0.1 - San Sas (2² +2²³)2 A(z) dx (1). [0,1]…

A: Here, in the question, two integrals are given. We have to explain why both the integrals do not…