valuate S. F · ds, where F(x, y, z) = (z, x, y) and c(t) = (t, t², t³), 0 < t < 1.

Q: f(x,y) = =dt V11-6t?

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Q: Find an antiderivative F (z) with F' (z) = f(z) = 2+18z2 +18z° and F (1) = 0. Remember to include a…

A: Answer and explanation is given below

Q: If f(x, y, z) = ln(xª + yl0 + 2³) + V (x10 + y8 + z4), then find fr, fy and f; at (1, 1, 1).

A: The given function is fx, y, z=lnx4+y10+z8+x10+y8+z4 and the given point is (1, 1, 1). Evaluate fx…

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 &amp; x=2rcos θ , y=2rsin θ

Q: e function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant

A: The given function is f(x,y)=x-12+y-12 and subjects to the constraint x2+y2=8 the formula for the…

Q: Find fr, fy, and fz. f (x, Y, z) = z In(x°y²cos(52)) fa = fy = fz = ||

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Q: Use the Chain Rule to find dz/dt if z= (x+y)e^x, x= 2− t^2, and y=t

A: Given that: z=(x+y)ex,      x=2-t2 and y=t

Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: 2 dy = t(i+t=) sec>x dt

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Q: riable t. If 2sin (x)+4cos(y)=3a dy and dt 3, what is the val

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Q: The maximum rate of change of the finction f(x, y, z) =x In(yz) at (1;2;5 is equal to: O None of…

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Q: valuate S S Se(3 – 4x)dV, whe e xy-plane defined by 0 < x s

A: To find: ∫∫∫E(3-4x) dV

Q: Evaluate f, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 <y< 1, 0 < z < x+y}.

A: According to question,Q = x,y,z : 0 &lt; x &lt; 2y, 0 &lt; y &lt; 1, 0 &lt; z  &lt; x+y

Q: Find the total differential of the function f(r, y) = (3 y²+6 2):

A: Given,           The function is fx,y=3y2+6x13 .

Q: Find the extrema of the function f (x, y) =x² + y² + x²y + 4 in the domain D={(X, Y), 1X1 <1, iyi <…

A: See the attachment

Q: Use chain rule to find dz/dt z=cos(x+2y), x=6t^3, y=7/t

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Q: Compute fe F d where F (x, y) = x² + y). (2xy + x, Hint: Is F conservative?

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Q: Xyz f(x.y.z) = function is given dt P(2,t,) in point fax + fy + f2z colculate.

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Q: Find a linear approximation to the function f(x,y) at the indicated point. 2x°y f(x,y) = at (5,1) 1…

A: Linear approximation to the function f(x ,y) at (a, b) :       L(x ,y) = f(a ,b) +(x-a) f x (a, b) +…

Q: Find the (absolute) maximum and minimum values of f(x, y) = sin x cos y on the square R = {(x, y)|0…

A: Given,            f(x, y)= sinxcosy                    (1) on the sqaure             R=x, y| 0≤x≤2π,…

Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

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Q: Find fa and fy. ay f(x, y) = 9e* dt f„(x, y)

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Q: f(x, y, z) = e-3zyz 三 fy = 三 ニ f.

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Q: Find f, (x,y) and fy (x.y), and explain why f(x,y) has no local extrema. f(x.y) = 8x + 3y + 4. fy…

A: It is partial derivative

Q: Find fr and fy. 2e" dt f (x, y) = 2, f.(r, y) = f„,(x, y) =

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Q: xsin-(x) If x =0.03 and y = 0.62, then value of C in the antiderivative of F(x) = is V1-x2

A: Given  F(x) = x sin-1(x)1-x2

Q: Find fr and fy. f (x, y) = 4e" dt f(x, y) = f,(x, y) =

A: A detailed solution is given below.

Q: * If z = f (x, y); then its total differential can be expressed as дz dydz date - ( 7 ), v + ( ;) -…

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Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

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Q: Find fz and fy- Te dt f(x, y) = 5 f.(x, y) f,(x, y) : %3D

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Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

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Q: Find fyy for f(x, y) = e* In(y).

A: The given function is fx,y=exlny.

Q: (d) The function x²+y? Vx2+y? (x, y) # (0,0) f(x, y) (x, y) = (0,0) is continuous at (0,0).

A: Note: according to Bartleby policy we are allowed to write only one question please post remaining…

Q: [2xy + yz (i) F(x,y, z) = x2 + xz with domain R³. || xY

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: b) f(x): 1 + sec2

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Q: Use the Chain Rule to find dz/dt. z = x2 + y2 + xy,    x = sin(t),    y = 3et

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Q: e-(z-1)2-y 1 (r, y) # (1,0) If f(r, y) = (I-1)2+y (r, y) = (1,0) %3D is continuous at (1,0), what is…

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Q: Using the Chain Rule, find dz/dt for z In(x? + y²) and x = t, y = t²

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Q: Find fz and fy- f(1, v) = | 3e dt f (x, y) =| f,(a, v) = [

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Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

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Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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Q: xsin-1(x) is If x =0.1 and y = 0.11, then value of C in the antiderivative of F(x) = V1- x?

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Q: (d) The function x²+y? Vx²+y? (x, y) ± (0,0) f(x, y) = (x, y) = (0,0) is continuous at (0,0).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Q1) Evaluate SSS, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 < y < 1, 0 < z < x + y }.

A: Since you have asked multiple questions, we solve first question for you. For other question to be…

Q: Find f and fy- f (x, y) = 9e dt f (x, y) = %3D fy(x, y) =

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Q: sume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

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Q: dz dt || z = cos(x + 3y), x = 8t³, y = 9/t

A: By the use of chain rule we need to find the required derivative.

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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