Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.6 Iterations x, #28 · Calculus · Applications of derivatives

Solve … in 29–32 by the iteration …, to find a …

Start the cobwebs for $x_{n + 1} = sin x_{n}$ and $x_{n + 1} = tan x_{n}$ . In both cases $d F / d x = 1$ at $x^{*} = 0$ . (a) Do the iterations converge? (b) Propose a theory based on $F^{''}$ for cases when $F^{'} = 1$ .

Solve $f (x) = 0$ in 29–32 by the iteration $x_{n + 1} = x_{n} - c f (x_{n})$ , to find a $c$ that succeeds and a $c$ that fails.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.6 Iterations x, #28

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