35. f(x, y) = x² + 2y² – x; R is the disk x? + y? < 4.

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…

A:

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: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

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.…

A:

Q: Find the maximum and minimum values attained by f (x,y, z) = xyz on the unit ball ² + y² + z² < 1.

A:

Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A:

Q: 2. Suppose that f (x, y), g(x, y) are two continuous functions on the xy plane. Is it true that So…

A:

Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

A:

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

A:

Q: 5. Conclude on the limit of f(x, y) = +v4 xy2 as (x, y) → (0,0) along paths y = mx and x = y?

A:

Q: Show that the opelator Tilol defined by Y=19;)=Tx.-E] *=(h:)is Linear and bounded

A:

Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

A:

Q: Suppose that the plane tangent to the surface z = f(x, y) at (-4, 2, 5) has equation z + 5x + 4y =…

A: From the equation of tangent, we can derive: z = -(7 + 5x + 4y) Hence,

Q: DNE.) +2+ f defined on |-1,3] maximum (x, y) = minimum (x, y) = Need Helo?

A:

Q: Bounded by the cylinders z = 2x2, y = x² and the planes z = 0, y = 4

A:

Q: A surface x(y, z) is defined implicitly xy + yz +x'z' = 3-xZ Calculate ду

A:

Q: # 4. Evaluate the line integral | (x +2x²y) ds, where C is the upper half of the unit circle x2 + y2…

A:

Q: Evaluate f(x,y,z) dS 2. 3DX²+4y+z on the surface S {(x,y,z):05xS2, y= 3, 1Sz5 4)

A:

Q: Compute (ax + by² + cz) dS over the sphere x +y +z² = 1.

A:

Q: 9. Evaluate the line integral / (2x – 3y) ds; where C is the line segment from (-1,0) to (0, 1)…

A: 9.

Q: 5. Are there any points on the graph of x2 - y? – 22 = 1 where the tangent plane is parallel to the…

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.

A:

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: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

A:

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: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

A:

Q: 2. Calculate (y+ z)dx+(x+z)dy + (x+ y)dz , where C consists of line segments from (0,0,0) to (3,2,4)…

A:

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: B. Use Green's theorem to evaluate f (x²y)dx + y²dy Where C is close path formed y = x and y = x³…

A: Above first question is solved. Solving more than one question is against the policy of bartleby.

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

A:

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

A:

Q: 4. Let f(x, y, z) = e² + zy² and let C be a straight line segment connecting the points (4,2,1) and…

A:

Q: Evaluate the line integralf, (xy + z)ds along the line segment C from (1,2,3) to (-1,1,5).

A:

Q: Show that the function u = p(xy) + Vry v(y/x) provides the quation = 0. dy?

A:

Q: Find the line integral (4х — 5у) ds, where C is the semicircle y = 9 – x² traversed from (3,0) to…

A: Graph the semi-circle. Take x=3cost and y=3sint Now, x'=-3sint and y'=3cost The angle covered by…

Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: 20- What is the share of the formula that allows calculating the y coordinate of the center of…

A:

Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y − 2) 2 = 2x − 2, S4: x = 0, S5:…

A: Consider the surfaces  S1: 2x + 3z = 6, S2: y = 2S3: (y − 2)2=2x − 2, S4: x = 0S5: y = 0S6: z = 0

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

A:

Q: 5) Consider the surfaces S1 : ryz = 10 and S2 : z =r² + y and the %3D point Po = (1,2,5).

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: Let y = 3x + 2x + 4. If Aæ = 0.4 at x = 1, use linear approximation to estimate Ay %3D Ay 2 Submit…

A:

Q: Calculate S. xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to (1,3).

A: We have to calculate the integral ∫Cxydx+3y4dy Where C is the curve in the xy plane, x=y2 from 0,0…

Q: *6. Let f: R' →R be given by =+4x'z-6xyz+4y-3x'y. Is M=f-((0}) a smooth surface (2-dimensional…

A: Given, fxyz=z2+4x3z-6xyz+4y3-3x2y2 Now, writing the given function in matrix form.…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.