Draw a picture on the z-plane

Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

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: Prove that for any point (a, b) ≠ (0, 0) on the parabola y = x2 , the normal line intersects the…

A: The given equation of parabola is y=x2  For the point (a,b)≠ (0, 0), the slope of normal is and at…

Q: For the function f(x,y,z) = In (10x + 7y + 6z), find fy, fy, and f,.

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Q: Find the asymptoles of the funchon given Hx)= x²- 5x+6 below X-2

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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: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

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Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

A: If be a positively oriented,  closed curve  enclosing the region D Then for a vector field F→=P,Q…

Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

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

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Q: Find the plane thst passes through the equation of. the point P(6,0,-2) ¢ = 1+t, z=2 -t entains the…

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Q: 3. Verify that u(x, y) = x² + 4.x – y² + 2y is harmonic and find %3D - a) the harmonic conjugate…

A: See the attachment

Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: c) Find the second degree polynomial approximation to f at (a, b) = (1, – 2) T2(x, y)

A: Given :- The second degree polynomial approximation to f at a,b = 1,-2 f x,y = -x2y2x2 +y2

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: 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: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

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Q: The orthogonal trajectories to the family of hyperbolas xy= C is given by the family 1)y=cx 2)y2 -x2…

A: We need to find the orthogonal trajectory to the family of hyperbola xy=c

Q: The local linear approximation of (1- x)2° at x, = 0 is a) 20 - x c) 20 +x b) 1- 20x d) 1+ 20x

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Show that u(x, y) is harmonic in some domain. u(x, y) = 2x – x³ + 3xy?

A: since Uxx+Uyy=0, then U is harmonic

Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

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Q: 4. Let f(z) = 1 23 1 - and find [ f(z) dz, where C a circle of radius 2 about the origin with…

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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) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

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Q: Find a point zo where the function f (z) = (z – 8 – 10i) (z – 8 – 10i) is differentiable. What is…

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Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

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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: The harmonic function for f(z) = u(x,y) + iv(x,y) to be analytic are:

A: Given that: f=u+iv

Q: Let F(t) = %3D F(t)dt (don't include the +C) Find

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Q: Verify Green's Theorem for: f4y³dx-2x²dy where C, oriented anti-clockwise, is composed of the…

A: To find the integral ∮C4y3dx-2x2dy where C is the positively oriented closed curve x2+y2=9, y≥0 and…

Q: | Let w=z² Find the image of the first quadrant in Z-Plane 2

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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: (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: 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: 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: Determine the linear approximation of f(x) = x* at x = 1. а. у %3D 4x - 3 O b. y=- 4 x - 3 О с. у-…

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Q: Let f(x, y) = 8+ 76xy+38x2 + 240y + . Find and classify the critical points of f.

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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: Let I(3m) and I(m) be the approximations of I f(x)dr obtained by the composite trapezoid rule using…

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Q: Consider the parabola f (x) = x² – 4x and the line g(x) = –2x – 1. Determine the %3D point(s) of…

A: Given parabola,y=x2-4x                     (1)Given line y=-2x-1                     (2)Put value of…

Q: for the function f(Z) z²-2z find the (z+1)° (2 t4) residues at singular points.

A: The residue of f(z) is solved below

Q: Find the asymptoles of the funchon given below Hx)= x²- 5x+6 (x-2) Cx+3)

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Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

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Q: Given the interval [a,b] that saitisFies the hypothesis of Rolle's Theorem For the Furnction f(x) =…

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Q: X+Z+3Siny X +2y-2

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