Consider F and C below. F(x, y, z) = (y²z + 2xz2)i + 2xyzj + (xy² + 2x²z) k, C: x = Vt, y =t + 8, z = t2, 0sts1 (a) Find a function f such that F = Vf. f(x, у, z) %3D (b) Use part (a) to evaluate F• dr along the given curve C.

Q: Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of…

A:

Q: Find the real values of ,a,b,c that make the convolution equal to zero for the vector function F(x,…

A:

Q: Find V. (F x G), if F(x, y, z) = 16xi +j+8yk and G(x, y, z) = xi + yj - zk.

A:

Q: Let v = (2, (2, 3, 2) 3,

A:

Q: Evaluate Əw at (u,v) = (1,2) for the function w(x,y)=xy-y²; x = u-v, y = uv. ди OA. -1 B. 3 O C. 1…

A:

Q: 15.8 Consider the equation x³ + 3y² + 4xz² – 3z²y = 1. Does this equation define z as a function of…

A: Given:  The equation: x3 + 3y2 + 4xz2 - 3z2y = 1. To define: z in the equation as a function of x…

Q: Let fx) = x + 2x and g(x) = x- 5. a) Find (f ° g)(x). f(x+h) – f(x) b) Find the difference quotient…

A: Given

Q: Show that ƒ(z) = 3x² + 2x − 3y² − 1 +i (6xy + 2y) is differentiable at every point in the plan -

A: The given function is f(z)=3x2+2x-3y2-1+i(6xy+2y)...(i).

Q: Differentiate: 3 a) F(y) = ( (y + 5y³) x²e* b) f (x) : x2+ex А c) f (x) : B+Cex

A:

Q: Another derivative combination Let F = (f. g, h) and let u be a differentiable scalar-valued…

A:

Q: Calculate Duf(-1, 1, 1) in the direction of =--23-k for the function f(x, y, z)=-4x² + 5xy + y² + 3x…

A: Given function is f(x, y, z) = -4x2 + 5xy + y2 + 3x + 3yz - z2 - 5xz

Q: Sketch a contour map of the function. f(x, y) = x² + 7y² y

A: The given function is .To determine the contour map and the sketch of the function.

Q: Let f(z) = x? + iy² where æ and y are the real and imaginary parts, respectively of z and C is a…

A:

Q: Consider Flx,y) = (3x2 +6y) i t (6x +4y%)j. (as Show that Fis lonservative a function Such Line…

A:

Q: Find and sketch the domain of the function f(x,y) = cosx + V3x-y+2

A: The given function is .The objective is to find the domain of the function and sketch the domain.

Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

A:

Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

A: Given function:To find Known facts:

Q: Find the linearization of the function f(p, q) = Pat (0,0) p-1 q+1

A:

Q: luate Sa F . = 3x² i + (=

A:

Q: Given scalar functions A = A (x, y, z) and B = B (x, y, z) Find the value of the expression

A: Find the value of the expression.

Q: C: r(t) = (t2 + 4)i + (t2 – 1)j + (t2 – 2t)k, 0sts 2 (a) Find a function f such that F = Vf. f(x, y,…

A:

Q: Let f (z) = ² + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

A: Real part of complex number

Q: For the given function f(x,y)=x²y³+3x³y, find a flay

A: