Let f(x,y)=x°-4y where 0

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

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Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: Let I = L,x? cos(x + 1) dx. The approximation of I using the two-point Gaussian quadrature %3D…

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

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Q: The linear approximation at r = 0 to sin(2x) is A+ Bx where A is: and where B is:

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Q: Find the external in the isoperimetric problem of the extremum of subject to f(y² +xy'- :“)dx= 2,y…

A: Consider the functional  Iyx=∫x1x2Fx,y,y'dxwith the conditions yx1=y1 , yx2=y2and Iyx=∫x1x2Gx,y,y'dx…

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: 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: Integrate the function f (z) = (z – 8i)- from z = 0 to z = 4 + 4i along the line x = y.

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Q: dz 2. Given z = 4x2 + y²,x = sin t, y = t², find- %3D dt

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Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: Let f(x) = e2sinz 1. Use the local linear approximation of f at x = 0 to approximate e2 sin(0.01

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Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

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Q: After using z = X - y as substitution, the DE (x-y)^2 * dy/dx = a^2 (a is constant) transforms to…

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Q: Find the function L that linearly approximates f at the given point. a. f(x,y) = X2+y2; (0,0) b.…

A: Refer to the question, we have to find the function L that linearly approximates f at the given…

Q: Find the linearization L(x, y) of the function f(x, y) at P0 Then find an upper bound for the…

A: We need to determine the linearization of the function: f(x, y)=xy2+ycosx-1 at P01, 2 over R:…

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: (Xy,Z)%3Dex(cosy +sinz) fr?, fy =?

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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: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: Use a local linear approximation of the function f(x) = VI cos[(V2x)T] approximate v3.98…

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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: 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: The linear approximation at z = 0 to sin(4z) is A+ Bz where A is: and where B is:

A: Linear approximation is found by L(x)=f(x)+f'(x)(x-a) Differentiate L(x) with respect to x.…

Q: where t is a non-zero parameter. Show that dx 28 Given that x=z and y==. 1+r Hence find its value at…

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Q: Find the linear approximation to f(x)= cot (x) LCx) = f (a) + f'Ca) (x-a). near a=" as

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Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

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Q: |dx + N(x,y)dy = 0 x² + y,

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Q: Use a local linear approximation of the function f(z) = VI cos[(V2r)] at some approximate v3.98…

A: To use local linear approximation of the below function to approximate 3.98cos7.963π. fx=xcos2x3π

Q: dy Give the coordinates of the point where dt y = sin(t)- t³ O (0,0) O (0.535,0) O (-0.535,0) O (0,…

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Q: Find an interval where the IVP dy (In t) + y = cot t dt y(2) = 3 has a unique solution.

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Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

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

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Q: Find g: R R, continuous in [0. ) and position in (0, ) satisfying g1) %3D )dt

A: Here we have,  g:R→R, continuous in [0,∞) and position in (0,∞) Also given g(1)=1 and…

Q: f x = sec(z) and y = tan(z) , then dy at z = dx 4

A: We can use the chain rule of derivative in order to solve the given problem.

Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: Given:           x3−2y2+xy=0,     (1,1)

Q: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

Q: . Use fourth order Runga Kutta Method to find y at x=0.1, given that dy = 3e* + 2y , y(0) = 0 and h…

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Q: Use the linear approximation of f(æ, y) = e+y at (0, 0) to estimate f(-0.03, -0.03)

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Q: Integrate f(x, y)= y cos xy over the rectangular 0 sxsm, 0 s ys 1*

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Q: Using an appropriate linearization, the local linear approximation of f(r) + sin z at 27 is f(x) SI

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

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Q: Let f (x,y) = sin(xy) + x² ln(y). fyx at (0,) is equal to: %3D А. 33 В. О С. 3 D. 1

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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: Using an appropriate linearization, the local linear approximation of f(z)= T+ sin z at 27 is

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Q: Exercise 6 Using the method of variation of parameters, the particular solu- tion y, for the DE y" +…

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Q: at at 4) Let t = ,u = x² – y² ,v = 4xy³. Find· ay əx

A: To find: The value of ∂t∂x, ∂t∂y. Given information: t=uv, u=x2-y2 and v=4xy3 Concept used: Quotient…

Q: Find the image of the line z =3 +iy under f(z) = e

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Q: Given z = 3x'y + V5 cos 2y-2x, detemine the total differential o

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Q: Let y sin(5x). If Ar 0.3 at z 0, use linear approximation to estimate Ay %3D Ay = = Find the…

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