Let V be the vector space of polynomials in x over R of degree ≤ 3 and define an inner product f. g = f f(x)g(x) dx for all f, g & V. You may assume that this makes V into an inner product space. Define the linear map a : V→ V by a(f)(x) = f(x) + xf'(x) where the f' denotes differentiation. Which of the following holds with respect to this inner product? Select one: O O O a is self-adjoint O a is orthogonal a is 'anti-self adjoint' meaning a* = -a O a Ia, where I denotes the identity map None of the others apply

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

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Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

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A: f(x) =3x2+2 f'(x) =limh→0f(-1+h) -f(-1)h        =limh→03(-1+h)2+2-3-2h        =limh→03+3h2-6h -3h…

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A: As per guidelines, I can answer only three subparts.

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A: Solution:-

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