Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.3 Tangent Planes and Linear Approximations, #43 · Multivariable Calculus · Partial derivatives

Solve … and … by Newton's method from three starting points: …

Solve $g = x^{2} - y^{2} + 1 = 0$ and $h = 2 x y = 0$ by Newton's method from three starting points: $(0, 2)$ and $(- 1, 1)$ and $(2, 0)$ . Take ten steps by computer or one by hand. The solution $(0, 1)$ attracts when $y_{0} > 0$ . If $y_{0} = 0$ you should find the chaos iteration $x_{n + 1} = \frac{1}{2} (x_{n} - x_{n}^{- 1})$ .

~11 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.3 Tangent Planes and Linear Approximations, #43

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.