Let f(æ) = VE = ai. For æo = 2.6, #1 = 3.4, x2 = 3.9, 23 = 4, æ4 = 4.5, %3D • What is the maximum possible absolute error if we use the Lagrange polynomial of degree at most two that interpolates f(x) at the three points æ0, #1, and æ2 to approximate f(3.7)?

a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. f(x) = 8x³/2, a = 1; approximate 8(1.73/2) a. p₁(x) = b. p₂(x) = c. Using the linear approximating polynomial to estimate, 8 (1.73/2) is approximately (Simplify your answer.) Using the quadratic approximating polynomial to estimate, 8(1.73/2) is approximately. (Simplify your answer.)

Q3. Using interpolation, approximate the following function by a polynomial of degree at most 3 using node points x; = i, i = -1,0, 1,2 : f(x) = 3x² – e*

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