3. Let C[0, 1] be equipped with the inner product (f, g) = f f(x) g(x) dx, where f = f(x) and g = g(x). →) Let f = x2. Find ||f||. answer. ) Let f = x² and g = (1-x)². Are x and y orthogonal in this inner product space? Justify your

Q: Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 +…

A: Let P denote the path that travels along with the graph of y=x2 from (0, 0) to (1, 1). Let f(x,…

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A: We will draw the arrow diagram for function mapping from set A to set B.

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Q: 3. Find the fixed point(s) of f : [1, 0) → [2, 0) defined by f(x) = vx² + x.

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Q: -If fand g are two scalar point functions then prove that div (fV g) =fV° g+Vf- Vg

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Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

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Q: 2. For F(x, y, z) = (6xsin y+10x=' )i + (3x² cos y-4ye* −2y²z³)j + (-2y³e² +15x²2²)k, find a…

A: Given Data: Let us consider the given data, Fx,y,z=6x sin y +10xz3i+3x2 cos y -4yeyz-2y2zeyzj…

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Q: If F(s) = 1/(S-2), then f(t) is %3D a) e²'u(t) c) u(t-2) d) e"'u(t) -2t b) u(t +2)

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Q: 3. Let f: R³ R be defined by f(x, y, z) =|| x ||. Find Vf(x, y, z). What is the domain of Vf?

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Q: INSTRUCTION: Prove or disprove 1. Show that f: R-{-}→ R-{} defined by f(x) 3x-5 = is bijective. 2x+1

A: Given :  f: ℝ--12→ℝ-32   defined by ;                f(x) = 3x-52x+1 To prove : f is bijective.

Q: 4. Show whether or not f is bijective. Letf : R → R_be defined as f(x) = I피+1 %3D

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Q: Consider the vector-valued function F(t) = exists. 21-6 In(-2) ²³-2t, 2-4t+3/ Find lim F(t), if it…

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Q: 1. Show that the following maping f are linear: f : R² → R² defined by f(x, y) = (x+ y,x).

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Q: b) If it is possible, find the function f(x, y) = u(x, y) + iv(x, y). where u(x, y) = x2 + 2xy- y²…

A: That's easy. Have a great day!!!

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Q: 5. Calculate the divergence of F = (7x², 9y, -52).

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Q: 8. Show that an isometric linear operator T: H→→ H satisfies T*T= I, where I is the identity…

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Q: Consider a function z(x, y) defined by the implicit relation x¹y+xz+yz² = 1. Determine the value of…

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