Q1. Locate and classify the singular points of the following functions: A: f(z) = z[1-e¹/z] B: f(z) = cot Z

Q: D) Consider a function f(Sv) of two variables, S and v. Assume that for S-103 and -0.1 we have the…

A: Given:To find:value of f(S,v) when S=103.5

Q: Q3:- Verify that the following functions u are harmonic, and in each case give a conjugate harmonic…

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Q: Find the domain of the following function. f(x,y) = cos X-2 .y + 1

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Q: Suppose that the temperature T at point (x, y, z) is given by T(x, y, z) = sin(xyz) and that an…

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Q: Find the x-coordinate of the point on the graph of f, between points P and Q, at which the line…

A: Let (x,y) be the point at which the tangent to f(x) is parallel to line PQ.

Q: Q1. Locate and classify the singular points of the following functions: A: f(z) = cotz. B: f(z) =…

A: Solution:-

Q: 2. Consider the functions f (x) 1 = - and g(x) = x² – 4 a) Let h(x) = (f ° g)(x). What is h(x)? b)…

A: Given query is to find the composite function and it's domain.

Q: Show that u = x³ – 3xy? is a harmonic function and find a corresponding analytic function f(z) = u +…

A: To show that u=x3−3xy2 is a harmonic function and to find a corresponding analytic function fz=u+jv.…

Q: 2. Check the following function f(z) = iz – 3z is analytic or not (Use C.R equations). 3. Compute :…

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Q: The owner of a skating rink rents the rink for parties at $240 if 20 or fewer skaters attend, so…

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Q: II. Consider the function g defined by 9(z, y) = cos (7z/T) logg(z Do as indicated. In what…

A: We know that the gradient of the function g contains the two vectors, one in the direction of x-axis…

Q: The Bay of Fundy in Canada has the largest tides in the world. The difference between low and high…

A: Given, Difference between low and high water level = 18 m  y = D + A cos (B(t - C))

Q: B.Verify that the real and imaginary parts of the following function satisfy the equation and that…

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Q: The solution of the linear congruence 4x = 5(mod 9) is? 6(mod 9) 10(mod 9) Qmod 9) 8(mod 9)

A: Since, x = 9 n + 8 and n element Z Now,  4x congruent 5 mod 9 implies  x congruent 8 (mod 9).

Q: 4. Let f(x, y, z) = = xy + exp (z)y + z. a. Find Vf. b. Let u = (-1, -2, 1) and a = (1, 2, log 7).…

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Q: U = e¯ª (x sin y − y cos y). -

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Q: implicitly by the equation y tan-1(xz) − x cos(yz) = 3. Find zy.

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Q: (i) Find fæ, fy, fry, far and fyy for the function: f(x, y) = e¹y² + x³y³ . Verify that fry = fyx.…

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Q: a. State the amplitude and period of the function f: R R, ƒ (x) = 3 – 6cos TEX Find the general…

A: Given function f(x) = 3 - 6cos(πx/4)

Q: Let D C R? be a domain. A real-valued function u: R→R, where (r. y) u(r. y) is called harmonic if…

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Q: Let z be a function of x and y defined implicitly from the equation 9ye" - 5 cos(y+ z – 1) = 7x –…

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