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# (Solved): please help number 2 & 3for all v, w ER" is an inner product on K. 4.1.6. Prove that for two vec ...

please help number 2 & 3
for all v, w ER" is an inner product on K. 4.1.6. Prove that for two vectors v, w in a real inner product || v + w || ² = || v || ² + || w || ² if and only if u and w are orthogonal. is hasis for n 5 space

1. Show that the linear minimax approximation to on is 2. The Legendre polynomial has a weight on which is defined by with . (a) Show that is an orthogonal family. (b) , dengan . 3. Define , where is a Chebyshev polynomial of degree . The polynomial is called the second type of Chebyshev polynomial. (a) Show that is an orthogonal family on with weight function . (b) Show that the family satisfies the triple recursive relation 4. For the integral with weight , find an explicit formula for nodes and weights from Gauss's quadrature formula and also give a formula for the error. 5. Boole's rule for calculating on an interval is defined by 6. Use Gauss-Laguere with and nodes to calculate the improper integral following:

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