14. We know that S(x,y)dx+g(x,y)dy] = Se f(x,y)dx + Se g(x, y)dy. Use this knowledge to evaluate S.y dx +x dy) wherec is the line segment from %3D (1,-1) to (4,3).

Q: c) Find i. y' for x4 + y = 17 If x = 3 and y = 3, calculate y'

A: Here is the solution of above problem.

Q: Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: Differentiate y = Væ + Vx + Væ. y =

A: We need to differentiate the given y with respect to x

Q: Find the antiderivative of the functions. S 6x dx S(12x - 5)dx S 3dx S(2x2 + 3)dx 1.) 2.) 3.) 4.)…

A: 1. ∫6x dx2. ∫12x-5dx3. ∫3 dx

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

A:

Q: Sketch the level curves of the function f(x, y) = 6-3x - 2y for c= -6, 0, 6, 1, 2

A:

Q: 29. f(x, y) = x + y, C: x? + y² = 4 in the first quadrant from (2, 0) to (0, 2)

A:

Q: iven function

A: In this question, the concept of integration is applied. Integration Integration is a method of…

Q: Find f, (2,0) if f(x,y) = 18x e Y. 1,(2.0) = %3D

A:

Q: Let X: EXP(0). suppose Y= 2x , the Y is i = 1 Select one: a. Gamma (n,-) b. Camma(n. 4) С.…

A:

Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

A:

Q: Find Vƒ(P) and D7f(P). (a) f(r, y, 2) = yf + z² – 4xz; Ū = } i – $ j+ k; P(-2,1,3)

A:

Q: D(3, 7) E(6, 1) F(20, 8) Is the line joining D to E perpendicular to the line joining E to F?

A:

Q: 11. The point (9, 16- A. (3,4)

A: y=f(x)after transformation y=f(x)(x,y)→(x , y)(9,16)→(9 , 16)=(9,4)

Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: + y = 2. What is y" at the point (1, 1)? y ² Suppose that x +

A:

Q: Find ƒxx ( x, y)  and ƒxy( x, y). ƒ(x, y) = 4x2e2y

A:

Q: dy Differentiate implicitly to find 6 5 3) x y+9x = 6y +4 dy

A: A detailed solution is given below

Q: Find ƒxx ( x, y)  and ƒxy( x, y). ƒ(x, y) = -3x2y3 + x3y

A: Given that, fx,y=-3x2y3+x3y Then we get,…

Q: Find y": Vy - Vx = Va

A:

Q: Select the option that gives a list of the stationary points of the function f(x, y) = x³ – 3x² –…

A:

Q: 2 The Range (Ry) of y = v9 – x² -

A:

Q: Find f, (8,2) if f(x.y) = e* - 5y.

A: We can find the answer as below

Q: Determine D,f (4,-1,6) for f(x,y,z) = ery + 4zx in the direction of (-3,2,6).

A: Given fx,y,z=ex2y+4zx3 in the direction of -3,2,6

Q: the doi n ain of the functions

A: We have given two functions : f(x,y)=1xy…

Q: Sketch the level curves of the function f(x, y) = = - y² for c= -4,-1, 0, 1, 4. 9

A: The level curves of a function f(x,y) are formed by plotting points (x,y) in the plane where f(x,y)…