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Computing Values of Functions

Weierstrass Approximation Theroem

Note: abs = absolute value Define f(x) = abs(x - 1/2) for 0 <=x <= 1. Use the proof of the Approximation Theorem to find an explicit polynomial p:R->R such that abs(f(x) - p(x)) < 1/4 for all x in [0,1]

Weierstrass Approximation Theorem

This question is about the Weierstrass Approximation Theorem Show that the Approximation Theorem does not hold if we replace I by R(real number system), by showing that if f(x) = e^x for all x, then f:R->R cannot be uniformly approximated by polynomials.

D'Alembert's formula

Utt means the second derivative with respect to t Uxx means the second derivative with respect to x Utt = 4Uxx, -(inf) < x < (inf), t > 0 U(x,0) = x, Ut(x,0) = xe^(-x^2) for -(inf) < x < (inf) Please use D'Alembert's Formula and show all work. If there is Fourier series, please show how you got eigenvalues and eige

Four stationary points of a multivariable function

A surface is described by the multivariable function f(x,y) where: f(x,y) = x^3 + y^3 + 9(x^2 + y^2) + 12xy a) Show that the four stationary points of this function are located at: (x1, y1) = (0, 0) (x2, y2) = (-10, -10) (x3, y3) = (-4, 2) (x4, y4) = (2, -4)