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1. Consider approximating integrals of the form

I ( f ) = &#8747; &#8730;x f(x)dx

in which f(x) has several continuous derivatives on [0, 1]
a. Find a formula

&#8747; &#8730;x f(x)dx &#8776; w1 f(x1) &#8801; I1( f )

which is exact if f(x) is any linear polynomial.

b. To find a formula

&#8747; &#8730;x f(x)dx &#8776; w1 f(x1) + w2 f(x2) &#8801; I2( f )

which is exact for all polynomial of degree &#8804; 3, set up a system of four equations with unknown w1, w2, x1, x2 and find the values

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This solution is comprised of a detailed explanation to answer Gaussian Quadrature problems.

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##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.