29. Show that the functions (x) = sin mx, m = 1, 2,... are orthogonal over the interval [-, ]. Construct the corresponding orthonormal set of functions.

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

Q: Let S = Span}( 3 2 3 . Show that dim(S)=2. 3

A: Basis: Let V be a subspace of ℝn. A basis of V is a set of vectors v1, v2, ..., vm in V such that:…

Q: The figure below shows the derivative F' of F. Let F (0) = 0. F'(1) ਜਿਹ 8 + 2 4 6 Of the four…

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: Letf :Z→Zbedefinedbyf(x)=x^2 +1,and letC ={1,2,3}. Find f (C), f ^−1(C), f ^−1(f (C)) and f (f…

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: Pron a. If u = f(x, y), where r = e' cost, and y = e' sint, show that (3)³ + (3) ² - - ² [(-)* +…

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Q: f" > 0 on (-∞, -1) U (-1,0).

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Q: 8(x) 48. f(x) 2 - x' In Exercises 51–60, show that f(g(x)) = x an dom x - 1 g(x) of 51,fx) = 2r + 1,…

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Q: Select the graph of a function f that satisfies f' 0 on (-0, -1)U(-1, 0).

A: means f is decreasing for x> - 1   means f(x) is concave up on both sides of x=-1

Q: Suppose (-8, 6) is a critical point of a function f with continuous second derivatives. If fra (-8,…

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