Problem 10: Let CR ([-1, 1]) denote the vector space of continuous real-valued func- tions on the interval [-1,1] with inner product given by (f.g) = [ f(x)g(x)dx. Let be the linear functional on CR ([-1, 1]) defined by y(f) = f(0). Show that there does not exist g € CR ([-1, 1]) such that y(f) = (f,g) for all fe CR ([-1, 1]).

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A: (.)  Leibniz rule :      Given ,(A).        where   and   .

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Q: * /Q1 = V4 – vx are: The domain D; and the range Rf of the function f (x) : D; = [0,16], R; = [0,2]…

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Q: f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...

A: We find the Taylor series of the given function

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Q: Oind Let g(2) = u(2)+iv(2) be ol complete function hiC →C, h(2) = e¯( v(a)+iu(2). Show that if h is…

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Q: (b). Let Y = {a, e, o, i, u}, take two relations R and S on Y and Prove that (SoR)-1 : R-1os-1.

A: composition of relations

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Q: 17. Let y₁ = x₁ + x₂ and y₂ = x² + x² + 2(x₁ + x₂ + x₁x₂). (a) Use the Jacobian to test whether…

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Q: Given f(x, y) and y = y(x), we can define a composite functiong(x) = f(x,y(x)).

A: a)Given , gx=fx,yx Then, g'x=∂f∂x+∂f∂yddxyx  [∵y=yx]⇒g'x=∂f∂x+∂f∂yy'x

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Q: = The real part for the function f (z) = 4z2 – 2z + 9 إجابتك = The imaginary part for the function f…

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Q: 7. Find if the following expressions result in a scalar or vector quantity or they are meaningless.…

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Q: 3x +1 III.(10) Prove that the function f: R – {5} –> R – {3} defined by f(x) = is a bijection. x- 5

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