Consider the standard inner product in the domain [-1,1]. Let f (x) : tan (a/4), g(x) = x + cos (a), h(x) = x?. %3D Which of the following are true: (1) f(x) and g(x) are orthogonal. (2) f(x) and h(x) are orthogonal. (3) g(x) and h(x) are orthogonal. O (1) only O (2) only O (3) only O (1) and (2) only O (1) and (3) only (2) and (3) only (1), (2), and (3)

Q: If u = 3x – x3 + 3xy? is a real part of an analytic function | f(z) = u + iv, where z = x+ iy is a…

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Q: a) Find the points at which the function f: C → C defined as: f(x + yi) = x³ − y² + (x − y)i - Have…

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Q: Given the functions Az) = cos(x) and g(z) = x - 5x- 6, determine the domain of the combined fx)…

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Q: en developing an exam schedule, the following data were colle 90 students study Advanced Functions…

A: Introduction: A Venn diagram is a diagram that uses circles to depict the relationships between…

Q: The function f(x) is invertible. Find (f-1)' (-8) given that f(x) = -x³ – 4x – 3.

A: f(x) = -x3-4x-3 We will use the formula for the derivative of the inverse function: f-1'x0=1f'(x0)…

Q: sy? is a real part z = x+ iy is a ce action v is

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Q: Let r(t) = (sin(t), cos(t), 6 sin(t) + 9 cos(2t)). Find the projection of r(t) onto the xz-plane…

A: Given vector…

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: (16) Show that: (1) The function f(z) is continuous in all complex plane. (2) (-1+i)-8(1+i).

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Q: a) Show that fi (x) = x, f2(x) = cos 2x are orthogonal on

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Q: Given the complex function ƒ(z) = |z|² = x² + y². Where are f(z) differentiable? Where is it…

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Q: 25. Find the harmonic conjugate of u = In|z| and corresponding analytic function f (z) = u + iv.

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Q: Img(:)=v(x.y) and g(-)=g: v(x, y) = 2x-2ry+sin xsly and g (0)=-1.

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Q: Let f(2) := 25. Show that f is invertible in a neighbourhood of i and calculate (f-1Y(/(i)).

A: Let f(z) = z5, show that f is invertible in a neighbourhood of i and calculate(f-1)' f(i)

Q: Given the complex function f(z) ee-iy. Where are ƒ(z) differentiable? Where is it holomorphic?…

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Q: If v(1, y) is a harmonic conjugate of a harmonic function u(1,y) is also a harmonic function. show…

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Q: 1. Determine whether the functions f1(x) = cos 3x, f2(x) = x, and f3(x) = cos² x are linearly…

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Q: Given that f(x) = 2x + cos(x) is a bijective function, find (f-')'(1)

A: The function f-1 represents the inverse of function f. Therefore, if f-1x=y then x=fy represents the…

Q: Let f(z) : D C be a complex function. Is it possible for both f(2) and f(z) to be analytic? 2. • If…

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Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

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Q: Let C, be the rectangle with vertices (0,0). (1,0) (0,2) and (1,2) oriented counterclockwise. Find J…

A: Green's theorem problem....

Q: Verify that the functions f1(x) = 1, f2(x) = sin x, and f3(x) = cos x are orthogonal in [−π, π], and…

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Q: Show that the function u = In(X² + Y2) is harmonic and find the conjugate harmonic v.

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Q: Let f. [-1/2,1/2] → R be given by f(x) = cos (x) * exp(x). There exists a unique inverse function g:…

A: We will use of chain rule