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Let ?(?) = ?^? on [−1,1]. Determine the interpolating polynomial of degree at most 2, c_2...

Let ?(?) = ?^? on [−1,1]. Determine the interpolating polynomial of degree at most 2, c_2 (x) , that interpolates f at the Chebyshev nodes (The zeros of ?_3 (?)). Evaluate the interpolating polynomial at x = 1/2.

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Answer #1

The Chebyshev nodes for are which come out to be

And we have

Interpolating at these points we get:

And so the polynomial is

Evaluating this at the point we get

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