Let f (z) = ² + iy² where x and y are the real and imaginary parts, respectively of z and C is a contour consisting of the line segment from z1 = 5i to z2 = 4 + 2i . Evaluate Re [f (2)] ?

Q: L is the straight line in the xy plane from (0,0) to (2, 2). Evaluate T, F.dr for each of the…

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Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: Find the linear approximation of the function f (x, y) = 2x – y+x?y - near the point (2,0). O 2x +…

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Q: Let f(x, y) = . Use the Linear Approximation at an appropriate point (a, b) to estimate…

A: Given,f(x,y) = x2y2+1To estimate,f(4.02,0.93) using the LinearApproximation at an appropriate point…

Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: Determine the linear approximation of f(x) = x' at x = 1. а. у3 9х +8 O b. Not in the list О с. у--…

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Q: Find the point in the plane x – 2y + z = 4 that is closest to the origin.

A: Solution)                   Given                           plane  x-2y+z =4

Q: Find the linear approximation to the equation f(x, y) = 3, zy at the point (6,2,6), and use it to…

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Q: Demonstrate that the functions Y1 = a", y2 = sin(x), Y3 = xe* are linearly independent on R. 9.

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Q: Let f(x, y) = x2 /(y2 + 1). Use the Linear Approximation at an appropriate point (a, b) to estimate…

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Q: Find the linear approximation at x = 0 to Write %3D 2- your answer in the form y = Ax + B. %3D

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Q: Use the Linear Approximation to f(x, y) = x/y at (9, 4) to estimate 9.1/3.9.

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Q: Evaluate f z²dz where C is the contour |z| = 2-

A: We can directly use cauchy Goursat theorem to give the value of the given integral about given…

Q: 1. Let F(x, y) = 1 0 if x + 2y ≥ 1 if x + 2y < 1 Does F defines the DF in the plane?

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Q: Let F(x, y) =x2+xyz+z , find at the point (1,1,1)

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Q: Consider f(x, y) = x³y+ 2xy? Approximate f(2.1, 1.03) by using the tangent plane.

A: Given f(x, y) = x³y + 2xy² Find f(2.1, 1.03) using tangent plane.

Q: Determine the linear approximation of f(x) = x² at x = 1. a. y= 2x +1 O b. y = 2x - 1 O c. y=- 2 x-1…

A: Given: f(x)=x2, x=1 To find: Linear approximation at given point.

Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

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Q: a. Find linearization of f(x) = Vx +1 at x = 7. b. Using your answer above, estimate V8.1.

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Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: Find a point zo where the function f (z) = (z – 8 – 6i) (z – 8 – 6i) is differentiable. What is the…

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Q: Find the linear approximation of f(x) = In r at a = 1 and use it to estimate In(1.14). L(2) = %3D…

A: Please refer the attached image for complete solution.

Q: YouTrylt 2 Find the linear approximation of the function f(x,y) =In(x- 3y) (7,2) at and use it to…

A: Please rate and feel free to ask any query about any part of the question.  Thanks

Q: Find the point at which the line f(r) = -z+1intersects the line g(z) = 4x +1 %3D

A: At point of intersection both the functions will have the same value therefore f = g

Q: Determine the linear approximation of f(x) = at z = 1. O a. y= 9x +8 O b. y=- 9 x-8 O c.y = 9x - 8 O…

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Q: Find the image of the line y =-x under the mapping = f(z) =2² + 4z %3D %3D

A: We need to find the image of the line y = - x under the given mapping.

Q: a²f If f(x,y) = e" sin (r + y), then prove that дхду дудх %3D

A: Hi! You have posted two non-related subparts. As nothing is specified, we are answering only the…

Q: Let  f(x)= x2+mx+c  , where m and c are constants. A(x) and B(x) are the linear approximations of…

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Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

Q: Find c so that the line y = 4x + 3 is tangent to the curve y= x^2 + c?

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Q: Find the value of c such that line y=3/2x+6 is tangent to the curve y=cx1/2.

A: Given,  line y=3/2x+6 is tangent to the curve y=cx1/2.

Q: Find the absolute maxima and minima of the function f (x,y)=2x²-4x+y²-4y+1 on the closed triangular…

A: Given:The given function is f(x,y)=2x2-4x+y2-4y+1 on closed triangular region bounded…

Q: Given f(x,y) = sqrt(x^2+4y^2) at point (3,2) find the linearization and use it to approximate…

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Q: Find the Direcctional derivatve of the function foxxy,z)=tan(xjz) aut point (t,2,4) in the direction…

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Q: By direct differentiation of x(t) = eAtxo + eA(t-o) Bu(o)do show that ¿(t) = Ax(t) + Bu(t), x(0) =…

A: The differentiation of a definite integral can be obtained by using the Chain Rule following…

Q: (b) If F = (5xy- 6x )i + (2y– 4x)j, Evaluate [F.dr along the curve C in the xy-plane, y =x' from the…

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Q: If T: R2 - R2 is the orthogonal projection onto the x-axis, then T-1: R2 R2 maps each point on the…

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Q: Evaluate F.dr, where F(x,y)=[2y-3cos(x)]i + [4x +6sin(y)]j and C goes counterclockwise around the…

A: The objective is to evaluate ∫CF·dr where Fx,y=2y-3cosxi+4x+6sinyj and C goes counterclockwise…

Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

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Q: Evaluate § F · ds, where F = 2x(x+y)i + (x² + xy + y?)j and the positively-oriented curve C encloses…

A: Here we will use greens theorem to find line integral of vector field For a vector field F→= Pi^+Qj^…

Q: Find the equation of the tangent plane to the graph of f(x, y) = 8x² – 2xy? at the point (5, 4). A)…

A: We first find the partial derivatives  So the direction vector of the normal is = (48,-80)

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: Find that F = 12x²yi + (4x + 8yz²)j + 8y² zk is conservative, and find a function f such that F =…

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

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Q: (a) Prove that the line 2x 3y + 26 =0 is a tangent to the curve x + y2 - 4x + 6y – 104 = 0 hence…

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Q: Find a function f:R² → R, its tangent plane at the point (1; 1; f(1; 1)) is given by -2x – 9y – z+8…

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