im(z,v) →(0,0) F(x, y).

Q: Consider the function f(x, y) = In(x² + y² + 1). 2 (a) Find Vf(1, 2). (b) Find Daf(1, 2) in the…

A: f(x,y)=ln(x2+y2+1) (a)Gradient vector…

Q: T(x,y, z) = x² + 2y² + z

A:

Q: Evaluate (xy + yz + xz)dV B = {(x, y, z) | 0 < x < 2,0 < y < 2,0 < z < 4}

A:

Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: Given f(x, y, z) = 2e(z+y), Find fy(0,},-4).

A: here we have to find partial derivative of a function w.r.t. 'y' and here we also use chain rule.

Q: Let f (x, y) = zy(z²–y") (z²+y²) if (x, y) + (0,0) and f (0,0) = 0. af af (a) If (x, y) # (0, 0),…

A:

Q: Suppose f(x, y, z)=x+y+z, h(x,y) = (x + y, x³, y) and g(x) = (x,x²). Calculate d =z=of oho g(x). dx

A:

Q: Consider f (x, y) = 5xy+ 7x³ + 10 a) Find f- (x, y). b) Find fzy(T, Y).

A:

Q: Find fa, fy, fz. f(x, y, z) x²y 2z+1

A:

Q: Let y(t)= r(t)-2r(t-1)+r(t-3)+u(t-4), where r(t) is the ramp function. a) plot y(t) (10 pts.) b)…

A: The objective of the question is to plot the function y(t), z(t) and y'(t) and calculate the energy…

Q: Given f(x, y) = 2x² + 3y³ + x²y A) Evaluate f(-2,1) f(-2, 1) = B) Find fz(x, y) fz(x, y) = C) Find…

A: A function is given which is dependent on the x and y and we need to find out the partial…

Q: Find r(t) if r' (t) = 5t+i + 7tºj + √√/ tk and r(1) = i + j.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Given f(x, y) = 2x² + 6xy² + y³, find frz(x, y) = fry(x, y) =

A:

Q: |dx + N(x,y)dy = 0 x² + y,

A:

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). r(t) = 2t²1 - 4tj + ²t³k (a) r(t) (b) r"(t) (c)…

A: Note that, according to Bartleby guidelines, we can answer only the first 3 sub-parts in the case of…

Q: x² + y² – 4 hat fa(x, y) = 2 Va² + y? · V9 - (Vx² + y? – 4) r2 |

A:

Q: ey f(x, y, z) = 2x / -42³e" + In (x³-2). Let f (x Find fx, fy and fz.

A: Step 1: Find fx (Partial derivative with respect to x)To find fx​, we differentiate f with respect…

Q: f (x, y) = 3y + xy – a² – y? Find Vf.

A:

Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

A: fx, y=x2y2 Partially differentiating with respect to x, we get ∂f∂x=2xy2 Partially differentiating…

Q: Let f(x, y) = 2x² + 4y² + 2xy+ 10x + 3y + 9 Find D = frr · fyy - i

A:

Q: Let f(x, y) =x+3x2y2, x(t) =t2 and y(t) =t3. Find F(x(t), y(t)) F(x(0),y(0)) F(x(2),y(2))

A: Let f(x, y) =x+3x2y2, x(t) =t2 and y(t) =t3

Q: f(x, y) =  5 xy +  xy 8; find fx, fy, and fyy

A: Partial derivatives

Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

A:

Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…