2. Show that f(t) = 1 – sint defines a smooth flow on the manifold S = ( (cost, sint) ), but g(t) =t – sint does not

Q: Use the Chain Rule to find the indicated partial derivative r= y +x cos(t), S = x+y : du du au when…

A: Here we have to find ∂u∂x, ∂u∂y, ∂u∂t. We have, u=r2+s2 .................................... (1)…

Q: Find the partial derivative of z with respect to u if: 2=x+4y, x= u sin v, y=u cos v

A: Partial differentiation

Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

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Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

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Q: Compute Scy dx + xy dy if C goes from (0,0) to (1,2) along the line parameterized as x = t, y = 2t.

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Q: Assume that x and y are functions of t. If y = x² + 4x and dx/dt = 4, find dy/dt when x = 1. dy dt…

A: Solve the following

Q: 2. Find the equation of the tangent plane and the normal line at the point (0 ,1 , 2) on the surface…

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Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: If U = lx+my,v=mx-ly then prove that partial derivative of x

A: Given: u=lx+my v=mx-ly   To show: ux=-vy and uy=vx

Q: In(xy) cos(Tx + T) when x 2 and y = 1/2.- Find the tangent plane to f(x, y)

A: We have to find the equation of  tangent plane.

Q: (b) Compute the partial derivative fy at the point (x, y) = (1, 1), or show that it does not exist.…

A: Let f:R2→R  be the function   F(x,y)=x-1.y-113(b) compute the partial derivative fy at the point…

Q: Compute the partial derivative of the function f(r, y, z) = e'-z cos(y) + z e=1/(1+y²) vith respect…

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Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

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Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

A: See the details solution in below

Q: 2. Show that f(t) =1 – sint defines a smooth flow on the manifold S = ( (cost,sint) ), but %3D g(t)…

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Q: Let z = z(x, y) be a continuous function of x and y defined implicitly by 1 sin(2'y* + y°z* + a*z) :…

A: Solve

Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y…

A: Given  By chain rule of differentiation , we have

Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: The student should estimate the equation 0.24 0.24 + tan [0.247 + 2(0.27)n] π 1 1 =-+-tan(Tx + 2ny)…

A: Given function: gx,y=xπ+xπtanπx+2πy Point: 14, 14 To estimate: 0.24π+0.24πtan0.24π+20.27π Formulas…

Q: Find dw/ds and aw/at using the appropriate Chain Rule. Function Point w = sin(5x + 6y) X = s + t, y…

A: According to guidelines we solve only first three parts.

Q: (1) Use the Chain Rule to find dz/dt. (a) z = r² + y² + xy, r= sint, y = e'. z = x2 +y?, x = cost+…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 4. Let f(x, y) = sin(x²y) + vx + e+y. Find the equation of the tangent plane to the surface z f(x,…

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Q: Find the length of the curve y = V cos 2t dt from x= 0 to x = 4

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Q: Consider h(x, Y, z) = cos (xy) + eY% + ln (xz). Determine the directional derivative of h at the…

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Q: Let f(x,y)=x•e. a. Compute all the first and second partial derivatives of f. b. Find the tangent…

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Q: Let y = 5,a. %3D Find the change in y, Ay when r = 5 and Ar = 0.2 Find the differential dy when r =…

A: Our problem is let y=5√x First, it is easiest to take the derivative of this when in a different…

Q: Suppose that the partial derivatives of a function f(x.y.z) at point on the helix x=cost, y=sint,…

A: In this question, we have given the helix and first derivatives of f. x=cost, y=sint, and z=t and…

Q: Consider the closed curve in the xy-plane given by x² + 2x + y* + 4y = 5. dy -(x+1) (a) Show that dx…

A: Given data:   The expression for the given function is x2+2x+y4+4y=5.   (a) Differentiate the above…

Q: Let y = tan(3r + 4). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: 1. Show that the problem may be formulated in terms of the velocity potential (r, 0) satisfying r dr…

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Q: Let z(x, y) = 2x2 3y2 where x = 2s – 4t & y = 9s + 8t. | dx dy ду az Calculate ds dz & and using the…

A: We have to find all first order partial derivatives.

Q: Compute the partial derivative: f(x, y) = sin(x® – 5y) fy(0, T) =

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Q: Suppose we have a surface f (x,y)=x²y+cos (4x) · Which of the following is the gradient of f(x,y) at…

A: First I have found the partial derivatives of f(x,y)  with respect to 'x' and 'y' at point P(π/2,…

Q: 1 The partial derivative of f(x, y, z) = Arctan with respect to z is xy? z³

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Q: 1)Consider the function f(x, y) = x° + 2xy + y? – 5x b) Calculate the second-order partial…

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Q: let it be f(x, y) = xy/x+y when æ > 0, y > 0 a) calculate the partial derivative at fr and f, at…

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Q: Use the Chain Rule to evaluate the partial derivative g at the point (r, 0) = (2/2, 7) where g(x, y)…

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

Q: Suppose that u = x²y, where x = r cos 0 and y = r sin 0. du Compute the partial derivatives du and…

A: Given that u=x2y  ….(1) where x=rcosθ  and y=rsinθ Differentiating (1) partially with respect to 'r'…

Q: Use the differential dy to approximate Ay whenx changes from x = -2 to x = -1.96. %3D y = x² + 1

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Q: 2. Sketch the streamlines for the flow u = ax, v = -ay, w = 0, where a is a positive constant. Next,…

A: Given the velocity is u=αx, v=-αy, w=0 and Lagrangian description is x=Xeαt, y=Yeαt, z=Z

Q: Compute the partial derivative: f(x, y) = sin (a- 6y) f,(0, T) =

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Q: Verify the linear approximation at ( 0, 0) for e^x cos(xy)

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Q: Determine the linearization of f(x, y) = arctan(x² + y²) at

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Q: Find the partial derivatives: af (x, y, z)/dx, f(x, y, z)/dy, df(x, y, z)/dz for the following three…

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Q: Q2) A) Verify that wxy = Wyx for w = x sin y + y sin x+ xy. B) Show that f(x, y) = e-y cos 2x…

A: Here we have to find the partial derivative of the functions with respect to x and y seperately…

Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

A: Given equation is s=x2+y2. Compute the derivative of s with respect to t.…

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

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Q: Find all partial derivatives of w = x sin(yz) – z In(xy)

A: To find all the partial derivative.