fc (y+z) dx (x+z)dy+ y2 dz, C consists of line segments from (0,0,0) to  (1,0,1)  and  (1,0,1)  to (0,1,2)

Q: Integrate f(x,y,z) = x + √y-2² over the path from (0,0,0) to (4,16,4) given by C₁: r(t)=ti+t²j,…

A: The objective is to integrate the given function f(x,y,z) .

Q: 12. In the xy plane the region D is bounded by the lines y = 2x + 6 y = 2r +1, y = -3r +6, and y =…

A: Given: y=2x+6 y=2x+1 y=-3x+6 y=-3x+1

Q: Evaluate | (transparent gamma symbol) ∫(x2 + y2) dz | where z = x + iy with (transparent gamma…

A:

Q: 1) Evaluate the line integral Fdr where F(x, y, =) = (x+3y, 2y +z, xy) and y: line segment from…

A: Here, F→(x,y,z)=x+3y,2y+z,xy and γ: line segment from (2,1,3) to (3,3,5) We need to evaluate ∫γF→dr→

Q: 17. Region bounded by y = 2x, y = x and x = 2. Rotate about: (a) the y-axis (b) x = 2 (c) the…

A: As per company guidelines we are allowed to solve maximum three sub parts so i am solving first…

Q: y2 %3D 1. 60. x²y dx dy dz, T: Region bounded by 4

A:

Q: I need help finding the absolute maximum and minimum values of f on the set D.

A:

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

A:

Q: dz (a) Use an appropriate form of the chain rule to find dx dz in terms of y in terms of x and if z…

A:

Q: 5. Evaluate the line integral (r+2y) dr+x² dy where C consists of line segments from (0,0) to (2, 1)…

A: In order to solve this question by the formula of line integral .

Q: Calculate the double integral (x + y)²ex* - y² dx dy where R is the square with vertices (2, 0), (0,…

A: According to the given information, it is required to find the integral over R where R is square.

Q: The region in the first quadrant is bounded by the curve y = 2 - x^2 and y = x^2. How far is the…

A: Given- The region in the first quadrant is bounded by the curve y = 2 - x2 and y = x2.  To find- How…

Q: y = In(3x), y = 1, y = 3, x = 0; about the y-axis V = Sketch the region. y y 4 6 4 4 6 X -1 4 y y 4…

A: The objective is to find the volume V of the solid obtained by rotating the region bounded by the…

Q: 2) The region is defined by y= sin x, y = 0, x= 0, x = T. Rotate the region about the: a) x-axis b)…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: 48. Let f(x, y, z) = xyz + 3. Find an equation of the level surface that passes through the point…

A: Given that: f(x, y, z)=xyz+3

Q: A heart-shaped graph in a 2D plane is defined by the equation (x² + y² - 1)³= 4x²y³ Determine dy/dx…

A:

Q: A function f has partial derivatives fx = 4x + y² - 6y +5, fy= 2xy - 6x. (a) Find the stationary…

A:

Q: Line WY bisects Line UV at Y. If UY = 2x + 1 and YV = x +7, find UV.

A: Meaning of biscsts is dividing into 2 parts .

Q: 3. Find the flow of F(x, y) = 10 – y along a semicircular curve as shown below. y C -5

A: The solution are next step

Q: Find both first partial derivatives. h(x, y) = e-(x7 + y?) %3D h,(x, y) = %3D h,(x, y) =

A: here we have to find the partial derivative.

Q: I need help finding the absolute maximum and minimum values of f on the set D.

A:

Q: f(x, y, z) = xe z2, piecewise linear path from (0, 0, 1) to (0, 2, 0) to (1, 1, 1)

A: To Determine: calculate ∫cxez2dx Given: we have piecewise linear path from (0, 0, 1) to (0, 2, 0) to…

Q: $ (ry + sin(r + y²)) dx + (3x²y+2y sin(x + y²)) dy, where C is the clockwise boundary of the region…

A:

Q: fze [sin(3x)]-m(x, y, z), where m(x, y, z) = Part C. yz-1 %3D

A:

Q: Q3A)Find normal line and parallel plane to the function f(x, y, z)=√xyz - 4 At point (1,2,8).

A:

Q: Evaluate the line integral |(3="y + (1- y):) dz + (z² – z2) dy + z(1 – y) dz where C is any curve…

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: 13. Region bounded by: y = 4 – x and y = 0. Rotate about: (a) the x-axis (c) y = -1 (b) y = 4 (d) x…

A: The solution are next step

Q: ds k(4nr). dt --Select-- %3D volume dV k dt surface are ds - ). dt dV dt dV = k(4tr²). dt

A: Given evaporation rate proportional to surface area Use formula of volume and surface area to find

Q: -1 -x and the curve x = 10 – 2y. 8 4. Compute the area of the region enclosed by the lines y = x and…

A: The solution are next step

Q: 2. The area bounded by y = -(x - 1)2 + 4, and the lines x =1, y = 2, and y = 4 rotated about the %3D…

A:

Q: Check cosh(xz)(z dx + x dz) for path independence. Does cosh(xz)(z dx + x dz) have path…

A: To verify whether the function cosxzzdx+xdz is path independent or not…

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

A: We will use parametric equation of lines to find the integral

Q: Find the linearization L(z, y) of f at the given point. Surface: f(a, y) In(x +9y) Point: (11e5,e)…

A: Given :

Q: (c) Evaluate the line integral 2.xycdx + (x-y)dy where C is from (1,3) to (0,0) along the parabola…

A:

Q: $(2xy - x²) dx + (x+y²)dy, where C is the enclosed curve of the region boundec. The value of by y=x²…

A:

Q: A function f has partial derivatives fx = 4x + y² − 6y +5, fy = 2xy - 6x. (a) Find the stationary…

A:

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

A:

Q: f (x,y)=arcsin( x²+y² -1)+x² +y² -1 %3D aşağıdakilerden hangisidir? (ə) D(x,y)={(x.y)|1<x² +y² <2} 2…

A:

Q: (b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line…

A: Given function is 3x+ydx+2y-xdy i) Given curve is y=x2+1 Hence the integrand becomes…

Q: Use Green's theorem to evaluate (2y dx - x dy) around the closed curve C. y (2,5) 4 3 2 C 1. -2 -1…

A:

Q: 2 |3x'e?" dx +5xr'e?" dy C:boundary of the region lying between the squares with vertices (1,1),…

A: We have to evaluate the line integral ∫C3x2e2y dx + 5x3e2y dy,C: is the boundary of the region lying…

Q: a) Evaluate the line integral S. (2x - y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

A:

Q: Q: Evaluate the closed line integral p y³dx – x³dy C Where C is the closed path from point A(1,0) to…

A:

Q: first order partial derivatives, i.e. dz/dx, dz/dy: xy³. z = In√√xy Z

A:

Q: Evaluate . y dx - x dy along the curve C shown in the figure below. y 4 y = x2 – 5x + 6 2 C3 2 C2…

A:

Q: 8. Evaluate the line integral (x'dx+ xe"dy where C is the closed path along the triangle in the…

A: Here we have to evaluate the integral ∫cx2dx+xe-ydy where C is the closed path along the triangle in…

Q: Integrate f(x, y) =x+y (4, 0) to (0, 4) over the curve C:x +y 16 in the first quadrant from %3D 32…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.