Let the function y(x) be defined implicitly from f(x, y) = y ln(1 - y) +...

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Let the function y(x) be defined implicitly from f(x, y) = y ln(1 - y) + x + 1 = 0. (a) Verify that the point (xo, yo) = (ln(2) - 1,-1) satisfies y(x) = yo. (b) Determine the 3-term Taylor polynomial of y(x) about the point xo. (c) For which values of x does y(x) exist uniquely? (d) (extra credit) Provide a plot of the 0 level curve of f(x, y). Let the function y(x) be defined implicitly from f(x, y) = y ln(1 - y) + x + 1 = 0. (a) Verify that the point (xo, yo) = (ln(2) - 1,-1) satisfies y(x) = yo. (b) Determine the 3-term Taylor polynomial of y(x) about the point xo. (c) For which values of x does y(x) exist uniquely? (d) (extra credit) Provide a plot of the 0 level curve of f(x, y).