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Calculus In Exercises 7784, find the orthogonalprojection of f onto g. Use the inner

Chapter 5, Problem 78

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QUESTION:

Calculus In Exercises 77 - 84, find the orthogonal projection of f onto g. Use the inner product in C[a, b]

\(\langle f, g\rangle=\int_{a}^{b} f(x) g(x) d x\)

\(C[-1,1], \quad f(x)=x^{3}-x, \quad g(x)=2 x-1\)

Text Transcription:

langle f, g rangle = int_a^b f(x) g(x) dx

C[-1, 1],     f(x) = x^3 - x,     g(x) = 2x - 1

Questions & Answers

QUESTION:

Calculus In Exercises 77 - 84, find the orthogonal projection of f onto g. Use the inner product in C[a, b]

\(\langle f, g\rangle=\int_{a}^{b} f(x) g(x) d x\)

\(C[-1,1], \quad f(x)=x^{3}-x, \quad g(x)=2 x-1\)

Text Transcription:

langle f, g rangle = int_a^b f(x) g(x) dx

C[-1, 1],     f(x) = x^3 - x,     g(x) = 2x - 1

ANSWER:

Step 1 of 3

We have to find the orthogonal projection of  onto .

We have to use the inner product in

We are given that

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