![Use the functions f and g in C[-1, 1] to find (f, g), ||f||| ||9||, and d(f, g) for the inner product (5, 8) - [F f(x)g(x)dx.](http://img.homeworklib.com/questions/3f7bb610-e425-11ea-99f5-15e3228ed7f9.png?x-oss-process=image/resize,w_560)
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Use the functions f and g in C[-1, 1] to find (f, g), ||f||| ||9||, and...
5) In C.), with inner product <f,g> [f(x)g(x)dx, let f(x) = x², g(x)= x', a) Compute<...
5) In C.), with inner product <f,g> [f(x)g(x)dx, let f(x) = x², g(x)= x', a) Compute< x², x? >; 0 b) Find the “angle” between the two functions.
Let f(x) and g(x) be any two functions from the vector space, C[-1,1] (the set of...
Let f(x) and g(x) be any two functions from the vector space, C[-1,1] (the set of all continuous functions defined on the closed interval [-1,1]). Define the inner product <f(x), g(x) >= x)g(x) dx Find <f(x), g(x) > when f(x) = 1 – x2 and g(x) = x - 1
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space C(I-1,1) of co...
NEED (B) AND (C)
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space C(I-1,1) of continuous real-valued funo- tions on the domain [-1, 1] (b) Use the Gram-Schmidt process to find an orthonormal basis for P2(R) with re- spect to this inner product (c) Find a polynomial q(x) such that for every p E P2R
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space...
Use the inner product <f,g>=∫10f(x)g(x)dx in the vector space C0[0,1] to find <f,g>, ||f||, ||g||, and the...
Use the inner product <f,g>=∫10f(x)g(x)dx in the vector space C0[0,1] to find <f,g>, ||f||, ||g||, and the angle θf,g between f(x) and g(x) for f(x)=5x2−9 and g(x)=−9x+2.
9. Suppose that we are given the following information about the functions f,g and their deriva-...
9. Suppose that we are given the following information about the functions f,g and their deriva- tives and integrals; =4 f(0) = 0 • f(1) = • f'(1) = 2 g(0) = 5 g(1) = 4 • g'(1) =-2 So f(x)dx = 8 5* |(x)dx = 5 Sa f(x)dx = 11 S3 f (x)dx = 6 (d) (5 points) Evaluate Si f(x)dx. (e) (6 points) Evaluate ( f (.5.1 + 4)d.. (f) (6 points) Evaluate, (ثم) (g) (6 points) Evaluate,...
5) In Coul, with inner product < f g >= $(x)g(x)dx, let f(x) = x”,g(x) =...
5) In Coul, with inner product < f g >= $(x)g(x)dx, let f(x) = x”,g(x) = x, a) Compute< x,x?>; b) Find the "angle" between the two functions.
QUESTION 9 Use the values given in the table for differentiable functions f and g to...
QUESTION 9 Use the values given in the table for differentiable functions f and g to answer the following questions. 3 f(x) f'(x) g(x) g'(x) 1 3 2 3 -3 2 5 3 1 -2 3 10 4 0 -1 (a) If B(x) = f(x) · g(x), find B'(3). (b) If M(x) = f(g(x)), find M'(1). (c) If P(x) = f(x3), find P(1).
4. (6pt) Use the inner product (f,g)f ds to determine the following. (a) Determine if the functio...
i need help with this linear Algebra question
4. (6pt) Use the inner product (f,g)f ds to determine the following. (a) Determine if the function g(z) = z2-3x + 2 or h(x) = x2-2x + 1 is closest to the fl () is closest to the function f)2+2 on (b, Show that (1,2r - 1) is an orthogonal set (c) Beginning with the basis (1,2 1, 2 (d) Find an orthonormal basis for P2. (e) Find the least squares quadratic...
2) The set S of all real-valued functions f(x) of a single real variable z is...
2) The set S of all real-valued functions f(x) of a single real variable z is a vector space. (a) Show that the set L of all real-valued linear functions f(x) = mx + b of a single variable x is a subspace of S. (b) Show tha (f(x), g(x))= | f(z)g(x)dx is an inner product on L. (c) Find an orthonormal basis for C with respect to the inner product defined in (b)
The functions f and g are integrable and atunciona tand g ara mag radio and Juste...
The functions f and g are integrable and atunciona tand g ara mag radio and Juste - - -. (vaser 28, and Loved - - 7. Une hes to completo parts (a trous f(x)dx = 8, and g(x)dx = -7. Use these to complete parts (a) through (9) a. f(x)dx = 0 (Simplify your answer.) b. 59(x)dx= [] (Simplify your answer.) c. J 69(x)dx = (Simplify your answer.) d. (1x)dx = 0 (Simplify your answer.) Joix) = f(x)]dx = 0...
5) In C.), with inner product <f,g> [f(x)g(x)dx, let f(x) = x², g(x)= x', a) Compute< x², x? >; 0 b) Find the “angle” between the two functions.
Let f(x) and g(x) be any two functions from the vector space, C[-1,1] (the set of all continuous functions defined on the closed interval [-1,1]). Define the inner product <f(x), g(x) >= x)g(x) dx Find <f(x), g(x) > when f(x) = 1 – x2 and g(x) = x - 1
NEED (B) AND (C)
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space C(I-1,1) of continuous real-valued funo- tions on the domain [-1, 1] (b) Use the Gram-Schmidt process to find an orthonormal basis for P2(R) with re- spect to this inner product (c) Find a polynomial q(x) such that for every p E P2R
2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space...
9. Suppose that we are given the following information about the functions f,g and their deriva- tives and integrals; =4 f(0) = 0 • f(1) = • f'(1) = 2 g(0) = 5 g(1) = 4 • g'(1) =-2 So f(x)dx = 8 5* |(x)dx = 5 Sa f(x)dx = 11 S3 f (x)dx = 6 (d) (5 points) Evaluate Si f(x)dx. (e) (6 points) Evaluate ( f (.5.1 + 4)d.. (f) (6 points) Evaluate, (ثم) (g) (6 points) Evaluate,...
5) In Coul, with inner product < f g >= $(x)g(x)dx, let f(x) = x”,g(x) = x, a) Compute< x,x?>; b) Find the "angle" between the two functions.
QUESTION 9 Use the values given in the table for differentiable functions f and g to answer the following questions. 3 f(x) f'(x) g(x) g'(x) 1 3 2 3 -3 2 5 3 1 -2 3 10 4 0 -1 (a) If B(x) = f(x) · g(x), find B'(3). (b) If M(x) = f(g(x)), find M'(1). (c) If P(x) = f(x3), find P(1).
i need help with this linear Algebra question
4. (6pt) Use the inner product (f,g)f ds to determine the following. (a) Determine if the function g(z) = z2-3x + 2 or h(x) = x2-2x + 1 is closest to the fl () is closest to the function f)2+2 on (b, Show that (1,2r - 1) is an orthogonal set (c) Beginning with the basis (1,2 1, 2 (d) Find an orthonormal basis for P2. (e) Find the least squares quadratic...
2) The set S of all real-valued functions f(x) of a single real variable z is a vector space. (a) Show that the set L of all real-valued linear functions f(x) = mx + b of a single variable x is a subspace of S. (b) Show tha (f(x), g(x))= | f(z)g(x)dx is an inner product on L. (c) Find an orthonormal basis for C with respect to the inner product defined in (b)
The functions f and g are integrable and atunciona tand g ara mag radio and Juste - - -. (vaser 28, and Loved - - 7. Une hes to completo parts (a trous f(x)dx = 8, and g(x)dx = -7. Use these to complete parts (a) through (9) a. f(x)dx = 0 (Simplify your answer.) b. 59(x)dx= [] (Simplify your answer.) c. J 69(x)dx = (Simplify your answer.) d. (1x)dx = 0 (Simplify your answer.) Joix) = f(x)]dx = 0...
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