, Consider the function f(x, y) = x'y + y – 27y. f has v at (3/3, 0). f has ? at (0,0). f has ? v at (-3/3,0). f has v at (0, -3). f has v at (0, 3).

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: Let I = f x*cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

A:

Q: Consider the one-form y4 W = dæ + (4 ln(10x)y³ + 13y) dy on {(x, y) E R² | x > 0}. If the one-form…

A: Given: The one-form…

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

A: NOTE: Refresh your page if you can't see any equations. . here we have the given function is

Q: Let f(x, y, z) = x'e sin(x yz) %3D 12 find dyəzd' x at the point (2, 0,0)

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: find du u = 0, v = 1 and dz of the function (z = f(x,y) = x² + y2), where x = ue" and y = ve" at dv

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Q: Given f(z) = | t2 – 16 dt 1+ cos²(t) OS At what value of a does the local max of f(x) occur?

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Q: Assuming - 6x° -y² + 7xy = 0 defines y as a differentiable function of x, use the theorem Fx to find…

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Q: For the function f(x,y,z) = In (5x + 7y + 1Oz), find f,, f, and f,.

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Q: Given the function ƒ (x, y, z) = V7y – 3x³ z, calculate the partial derivative with respect to y, in…

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Q: . We are given r'y-5x+24y 6/ỹ, where x and y are both functions of t. If dx = 2, x= 1, and y=9, what…

A: Given query is to find indicated derivative.

Q: dy For the function dt d y is 3 cos t, the third %3D order derivative dt3 O 3 cos t

A: Given: dydt=3cost To find the third order derivative d3ydt3. Solution: We have, dydt=3cost…

Q: Assume that x and y are differentiable functions of t. For the following, find  dx/dt given that x =…

A: Differentiate both sides with respect to t. For xy use product rule, then cancel 2 from both sides.

Q: Find the linearization L(x,y) of the function f(x,y) = e 3× cos (9y) at the points (0,0) and 0,

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Q: Find aw/as and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) X = s + t, y…

A: we have to find partial derivative by using chain rule

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

A: The solution is given as

Q: functions of t. For the following, find dx/dt given that x = 3, y = 9, and dy/dt = 2. y2 = 2xy + 27

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Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: Show that the function y(x, dy/at = a2y/ar2 = dy/ax = %3D %3!

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

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:…

A: We have the given function in x and y as 2xy-5x+3y3=-51 On differentiating both of the side with…

Q: 4x - 6xy? + 3y² = 228; dx = 3, x = -3, y = 4 %3D

A: Given  4x3-6xy2+3y2=228 ; dxdt= 3   at     x=-3    , y=4

Q: Find ow/@s and ôw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) x S+ t, y =…

A: Given that function w=sin2x+3yx=s+t , y=s-tvalue s=0 ,t=π2To find :∂w∂s,∂w∂tSolution…

Q: Find fr and fy- f (x, y): 6e dt 4 fa(x, y) = fy(x, y) =

A:

Q: Evaluate dW at t = dt for the function W = xy x = sin t, y = cos t, z = t². 4 49л2 972 9x2 4 49л

A: Given: W=xyz,x=sin⁡t,y=cos⁡t,z=t2 Substitute the value of x, y and z in w , we get W=sintcostt2…

Q: Assume that x and y are differentiable functions of t. For the following, find dx/dt given that x =…

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Q: For the functions z = f(x, y), x = g(t) and y = h(t), if g(1) = 3, h(1) = 2, g'(1) = –1, h'(1) = 2,…

A: To find- For the functions z = fx, y, x = gt and y = ht, if g1 = 3, h1 = 2, g'1 = -1, h'1 = 2, fxP3,…

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

A: Given y=3x2-5x a. We need to find the value of dy/dt when x=2,dx/dt=3. the value of dy/dt=21 when x…

Q: dw at t= dt For the functions w = - 4x + 10y, x= cos t, and y = sin t, express as a function of t,…

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Q: Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

A: Given problem:- Use Green's theorem to evaluate ∫c (xy + y2 )dx + x²dy  by the curve y = x and y =…

Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: The function f(z) =e² is: contiuous in C discontiuous in C Ou(x,y) =e*cos(y) Ou(x,y) =e*sin(y)

A: The function f(z)=ez the given function is continuous.

Q: -2 X Given f(x,y,2) sin (z²y), show that fxyuy = fyxy %3D %3D

A: Given:- f(x, y, z) =e-2x sin(z2y)  To prove:- fxyy = fyxy

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: w=x2+y2+z2,  x=cost,  y=sint,  z=et a).…

Q: Q3) For f(x,y) = Sin(x,y) find fryxy at (1,–). %3D

A: Given query is to perform indicated derivative operation.

Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

Q: For f(x, y)= e sin(25x), evaluate fy at the point (77, 0). Of,(7,0)=50 O fy(7,0)=0 Of(7,0)=51…

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Q: of and dy For the function f(x.y) = sin (2x - 5y), find dx of of

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Q: Evaluate dt dW at t=0 for the function W = e' – In x , x = t², y= In t

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Q: - Use Modified Euler method to find the function (y) when dy 0< x< 0.4, given that = y* + Vx, for…

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Q: Given f(z, y) = 7x° cos (y*), find fzy(z, y) = | fyy(T, y) = [

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Q: If y (x, t) is a function of x and t, prove that i) Lat =py (x, p)- y (x, 0) ii) L- = p°y (x, p) –…

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Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: Ql: f(x.y)-y cos xy over the rectangle 0sxs , 0 sys1

A:

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.: y2 - 8x3 = -55; dx/dt…

A: y2-8x3=-55, dx/dt=-4x=2,y=3

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

A: Given query is to find the derivative of x and y with respect to t.

Q: x + Y f(x, y, z) = x sin + e*% – 1

A:

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: The function w=xycosz, x=t,y=t2,c=arccost. Then we have to find dwdt(a) by using the appropriate…