Let ʼn be a positive integer and let u(x, y) = (x² + y²) Show that where C' is a constant depending on n. Find the value of C. C = (22²2 +2²2) 0(2, 1 u(x, y) (2,3)=23+(2,9) -u(x, y) y²

Q: Example: Calculate the value of (@w/0x) at the point (x, y, z) = (2, -1,1) if:- w = x2 + y2 + z? z3…

A:

Q: (a) Find the constants A, B, C, and D that satisfy 1 1 1+ (w/o)² 1 + ((z-w)/7)2 Aw B Cw D 1+ (w/o)²…

A: Use partial fractions

Q: Give algebraic proofs of properties (1)u + (-u) = 0 ,(2) (c + d)u = cu+ du

A: Let be a vector such that  Multiply  with -1. Adding the two results,  Thus,is the additive…

Q: + ax ax²y + bxy² + 2y³ be (x, y) its harmonic conj en la + b + v(1, 1) is ec

A:

Q: Prove that B(m, n) = B(m + 1, n) + B(m,n + 1)

A: given,

Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

A:

Q: Suppose z = x + iy and f(z) = z - 1. Find w = u + iv such that f(w) = 1 + 3i (A) 3+2i (B) 3-2i (C)…

A: We have given that , fz = z - 1 , where , z = x + iy Here , w = u + iv Let , fw = 1 + 3i We need to…

Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: Show that (0, 1) ~ R.

A: We need to show that the open interval (0, 1) and R( the set of real numbers) are equivalents. The…

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 16. Find the values of r so that the function y= e™ satisfies the equation y" – 4y' – 21y = 0. A)…

A:

Q: Find x, y, z values according to x(i+j+k)+y(i-j+2k)+z(i+k)=2i+k

A: x(i+j+k)+y(i-j+2k)+z(i+k)=2i+k  =>(x+y+z)i+(x-y)j+(x+2y+z)k = 2i+k Now, comparing the…

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

A:

Q: Let C be a constant. Consider Compute(a) da. ان | دن 3 7 3 73 ㅠ + CT 53 + СT 7 + СT 3 -x², f(x) 2) =…

A:

Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

A:

Q: Find a such that the distance from (−1, 2) to ax − y + 9 = 0 is √5 units.

A:

Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

A:

Q: let v = (1, 2, 4), u = (6, −1, 2), and w =(1, 0, −3). Calculate the given quantity.  v · (u × w)

A: v=(1, 2, 4)u=(6, 1, -2)w=(1, 0, -3)

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

A:

Q: Let sin(3x4 + 6y5) if (x, y) # (0,0) f(x, y) x² + y4 if (x, y) = (0,0) Which of the following…

A:

Q: Eliminate the Arbitrary Constant(s): 1. y = c,x2 + C2xe* 2. Iny = c, + C2x

A:

Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

A:

Q: Using the substitution u = (A) (B) C D 1+1 du [₁ -1/2 du [(u ¹/2 - u-1/2) d du (u - 1) / u-²1) x + 1…

A:

Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

A:

Q: A) B) dx₁ dt dx₂ dt dx₁ dt dx2 dt dx₁ dt dx₂ Wh = x₁ + 2x₂ + 2x₁.x2 = x₁ + x₂-X1X2 is stable or…

A: Given :           A) dx1dt=x1+2x2+2x1x2    dx2dt=-x1+x2-2x1x2           B) dx1dt=-x1+x2+x12…

Q: Let u= 31-2j + k and v= 2i – 2j + 2k. Find ux y.

A:

Q: Write the following equation in the form w = u(x,y) + iv(x,y) h(z) = (3z + 2i) / (2z2 + 4)

A:

Q: Write the following equation in the form w = u(x,y) + iv(x,y) h(z) = (3z + 2i) / (2z2 + 4)

A:

Q: (2xy + 3x²)e +(x² – 2yz + 2y)e,y- (e² + y²)e, olan f(x, y,z)

A: Given

Q: Let C be a constant. Consider Compute(a) da. ان | دن 3 7 3 73 ㅠ + CT 53 + СT 7 + СT 3 -x², f(x) 2) =…

A: