Let C be the unit square with diagonal corners at -1 – i and 1+i. Evaluate f(z) dz, where f(z) is given by the function sin z.

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

Q: Let f(z) = x² +iy² where z and y are the real and imaginary parts, respectively of z and C is a…

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Q: Find a,b and c so that the quadrature formula has the highest degree of precision f(x)dx af (0) –…

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

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

Q: Find a,b and c so that the quadrature formula has the highest degree of precision f(x)dx = af (0) –…

A: Given that ∫02f(x)dx≈af0-2bf1+3cf2 where a, b and c are constants to be determined. It is also given…

Q: B) Use Green's Theorem to evaluate F dr, where C is the triangle with vertices (0,0) (3,0) and (3,…

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Q: Find ▽ x (▽xF) if F(x, y, z)=10xy j+ 10ryz k.

A: The value of ▽ x (▽xF) is (10 + 10y)i + 10xj + 0k

Q: (a) R (T) = A cos @o T (b) R (T) = A sin on t (c) A - A (/to) which is a rectangular function of t…

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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: | f(t) dt = x*e* e + a

A: This question is based on integration.

Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

Q: Let z= I= 2e", and y = 3 ln v. Find in terms of u and v.

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Q: Given f(x, y, z) = x³yz². Find f.(1,1,1).

A: The equation we have , f(x,y,z) = x3yz2 We have to find out fz, Now we differentiate f(x,y,z) with…

Q: Find the absolute maximum and minimum of f(x, y) = 4x2 + 2xy 3y2 on the unit square 0 sx s1, 0 sy…

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Q: For the function f(x,y,z) = In (7x+ 2y +5z), find fy, fy, and f,. fx =口

A: Given,           fx,y,z=ln7x+2y+5z

Q: A. Evaluate F(s) by definition for (a t²), t≥ 0. B. Evaluate sin z z²+j2z dz, C the boundary of the…

A: As per our Bartleby rules we have to answer only one question, when there are two or more questions…

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

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Q: The function f (x, y) = xy satisfies Lipchitz condition on the rectangle R: x| < 3, ly| < 2. a) True…

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Q: Let I = f, x² sin(x + 1) dx. The approximation of I using the two-point Gaussian quadrature formula…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Evaluate p xy*dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,3), and (0,3)

A: *Concept:- Use Green's theorem.

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Q: If f(x,y,z) = In(xz) – 2xy2z, find fzxy at the point ( 0.5, 1,-1) a) 2 %3D d) – 2 e) - 4 g) None of…

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Q: If f (x, y) = x²y? + sin(ry), then fy (2,0) =

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Q: Show that the Cobb-Douglas function F(x, y) = bx" y" satisfies the equation ƏF ƏF + y (n + m)F(x, y)…

A: Given that the Cobb-Douglas function F(x,y)=bxnym We have to satisfies the equation…

Q: The function f (x, y) = xy satisfies Lipchitz condition on the rectangle R: x| < 3, ly| <2. a) True…

A: fx, y=x23y   ,   R: x≤3, y≤2 Consider, fx, y1-fx, y2=x23y1- x23y2         ⇒fx, y1-fx,…

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: For the scalar function f, div(grad f) is equal to Select one: a. + + dx?' ay? ' az? b. dx dy dz C.…

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Q: Given z = f(x – y, 2x – 2y, 3x – 3y). Show that dz dz 0. dx fie +

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Q: Write a in the form of a = a¡T + a„N at t = 0 without finding T and N for r(t) = (2 + t)i+ (t +…

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Q: Find a,b and c so that the quadrature formula has the highest degree of precision | f(x)dx af (0) –…

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Q: Given a function f(x, y, z) = cos (x + xy²z²), find: f#(5,1, 1) = frz (T, 1, 1) = %3D

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Q: Show that ||T(x)|| = ||x||, Vx E R². Show that T(x) · T(y) = x · y, Vx € R². Interpret the property…

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Q: If z=x+iy where x and y are real, find the real and imaginary parts of:- Z+1

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Q: Evaluate f ((x – y) cos(7(x + y))) dA where D = {(x, y) : Y < x < y+2, –x < y< 3 – 2}. D

A: Solve double integral by using the change of variables

Q: Let f(x, y) = x² + xy + y² where x = 3(t + s) and y = e2st, find . as

A: we have given f(x, y) where x and y are function of s and t.  We have to find the partial derivative…

Q: If F (x, y, z) = e^xz i + 3xe^y j − e^yz k, then find ∇.(∇ × F)

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Q: Let f (z) = ² + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

A: Real part of complex number

Q: Find fx and fy, and evaluate each at the given point f(x, y) = exy2,   (ln 3, 2)

A: Given:  f(x, y)=ex y2 ;    (ln 3,  2)To…

Q: Given f(x, y, z) = x In(yz³), find fay and fyz. %3D

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Q: If f(r, y) da dy = K, where K is a constant, then 5 f(x, y) dy da: %3D ок O-K

A: Solution: The objective is to find the value given integral

Q: Let F = (x + y) exp(x), x = ln(u), and y = v. Find Your answer should be in terms of , y, U, and v.…

A: We have to find partial derivative

Q: If f(z) = sin(z 2) = U(x, y) + iV (x, y), determine U and V . Verify that the C-R conditions are met…

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Q: If f(x, y) = xe"y – In(xy), then a f dxdy =......

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Q: (3) If | f(x) dx exists and c is a real constant, prove that f(2) dz = / f(x + c) dz. | {(x+c) Vel

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: If f(2) = sin(z?) = U(x, y) + iV (x, y), determine U and V. Verify that the C-R

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