If f(x, y) = (2x? + 8y²)í, then f_(0, 0) = %3D A) 0 В) 1 C) 4 D) 2 E) Does not exist

Q: Compute fx + fxy + fyyzz, where f(x, y, z) = z sin(xy)

A: Given f(x,y,z)= z sin(xy)

Q: Evaluate the line integral ſc 2y dx + 6x dy where C is the straight line path from (4, 1) to (6, 5).…

A: Given query is to find the integral.

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

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Q: Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r…

A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

Q: Let y = 2x + 7x +3. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay 2

A: Linear approximation

Q: 3. Show that the line integral + 2xy) dx + x² dy + 2xz dz, is independent of path in R3, where C…

A: We will find out the required value.

Q: Let f(x,y, z) = xtan (Vyz)- sin(e*) , evaluate zy %3D дудхда

A:

Q: 6. The solid bounded by x = y², and x = 8 – 2z2 – y?.

A: To find the triple integral over the given solid bounded by x=y2,x=8-2z2-y2.

Q: 20. Show that a²F(x, y) -dx dy дх ду over the rectangle xo < x < x1, Yo < y < y1, is F(x, у) — F(x0.…

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Q: Show that S f(x,y) dy dx = , f(x,y) dx'dy. %3D

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Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

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Q: UNIVERSIT b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz + = 0. dy

A:

Q: Let y = 5x + 7x + 3. If Ax = 0.3 at x = 3, use linear approximation to estimate Ay Ay =

A: Follow 2nd step.

Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

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Q: Provide an appropriate response. If xy + x = 12 and dx/dt = -3, then what is dy/dt when x = 2 and y…

A: We will find the value of dy/dt with the help of the given data x=2 ,y=5 and dX/dt=-3 as following.

Q: bounded by Y=x3, V=1x i rotare about X=1

A:

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: (a) 3y' In (u) dy

A: We will use the ILATE rule in this example to solve the integral and for solving we use the formula…

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = S [² f(x) dx + √° 9( g(x)…

A: Given the region is bounded by y = x3 , y = 2x+4 and y = -1. Intersection of y = x3 and y = 2x+4 is…

Q: Let y = 2x + 5x +. 2. If Ax = 0.4 at a = 4, use linear approximation to estimate Ay Ay =

A:

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion= = ["5(x) f(x) dx + dx +…

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Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: We have a paraboloid, and each cross section is a circle, parallel to the plane x = 5. We use…

Q: f(r, y, z) = byz In(4ry) %3D fz = fy = た=

A: Given:

Q: Let y = 4x? + 4x + 2. If Ax = 0.3 at x = 3, use linear approximation to estimate Ay Ay = Preview

A: Given:

Q: Evaluate the triple integral. 7x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: Here, E is the surface boiunded by the  paraboloid x=5y2+5z2 and the plane x=5. Now, at x=5,…

Q: u,v) = ve*tv, and z(u,v) = (u+v)cos v?. OG nd and by using multivariable Chain Rule method. du u=1

A: Given: Gx, y, z=e2x+y+3zxu, v=u lnu+vyu, v=veu+vzu, v=u+v cos v2  To Find: To find  ∂G∂uu=1v=0  and…

Q: Find over xlapping area two equatione also gemetrical nepresentahon 2. 4'+v?=n, u?+cV- vn)=1 whore n…

A: Given curves are,…

Q: t in 30 minute please duopoly with homogeneous goods. There ar

A: When there are only two firms in the industry, it is in their advantage to collude and set the price…

Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

A:

Q: Let f(x, y) = xcosy- y e*y. fxy at (1,0)is equal to:

A: For finding the Partial differentiation we need to take one variable constant and differentiate the…

Q: Lây ởy - Find the bounded solution of- ,x>0, t> 0 where y (0, t) = 1, y (x, 0) = 0.

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Q: The equation dy + v y² + ¢y+x = 0, dt where y, 4, and x are functions of t, is called the gen-…

A:

Q: The scalar path integral 3(16-a y-) ds, where the path C is the straight line from the point (0,0)…

A: This is a problem of line integral. Since the path given for line integral is embedded on the x…

Q: Show that the line integral 22 +2ry) dx + x? dy + 2xz dz, is independent of path in R, where C runs…

A: We will find out the required values.

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: The given equation of the cylinder us x2+y2=1 in the half space y≥0. Calculate the value of ∫∫∫xzdV,…

Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

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Q: Let f(x, y) = xcosy- y'e*y. fxy at (1,0)is equal to: %3D -2/3 -2 1 0.

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Q: Q2:show that the force Fexyzi-x4z'k is Conservative. ?

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Q: (3) +. R Ris bounded by the semicircle y = V2x – x² and the line y = x

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Q: Let y 4x + 3x + 4. If Ax 0.3 at a = 3, use linear approximation to estimate A %3D Ay =

A:

Q: Let y = 4x + 2x + 4. If Ax = 0.1 at x = 2, use linear approximation to estimate Ay %3D %3D Ay 2

A:

Q: || | /3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8. %3D

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Q: Let y = 4a2 + 8x + 2. If Aæ 0.4 at x = 5, use linear approximation to estimate Ay %3D %3D Ay =

A:

Q: 2x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the plane x = 2. %3D

A: The given integral is ∭E2xdV. The region E is bounded by the paraboloid x=2y2+2z2 and the plane x=2.…

Q: integrate t dt/(1-ct) where c = const.

A: Solved below

Q: 2. Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xyax - (4y + 2x2)a, + 8zaz. Use…

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Q: (R, d), where d(r, y) = |r – y|, is separable. %3D

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Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

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Q: 2)Evaluate er dA , Ris bounded by y = x2,y 1 3)Evaluate I| Vy2 + 1dA , Ris bounded by x = 4 - y? ,x…

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