) Find quadratic least-squares approximation to f (x) = 2*, using ii) Chebyshev polynomials, and
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- (a) find the least squares approximation g(x) = a0 + a1x of the function f, and (b) use a graphing utility to graph f and g in the same viewing window. f (x) = sin 2x, 0 ≤ x ≤ π / 2Find the least squares approximation g(x) = a0 + a1x of f (x) = ex, 0 ≤ x ≤ 1.(a) find the least squares approximation g(x) = a0 + a1x of the function f, and (b) use a graphing utility to graph f and g in the same viewing window. f (x) = sin x, 0 ≤ x ≤ π / 2
- Apply Newton’s method to estimate the solution of x3 − x − 1 = 0 by taking x1 = 1 and finding the least n such that xn and xn+1 agree to three digits after the decimal point.(a) find the least squares approximation g(x) = a0 + a1x + a2x2 of the function f, and (b) use a graphing utility to graph f and g in the same viewing window. f (x) = √x, 0 ≤ x ≤ 1Expand x^2y+3y-4 about the point (-1,2) by Taylor's theorem
- 2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.What does it mean for the differentiability of a function if only one of the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) holds?