All the worked exercises of the chapter: applications of Newton’s method (roots, reciprocal, linear functions), classification of discontinuities, determination of parameters for continuity and differentiability, the zero theorem with bisection and counterexamples to Weierstrass’s theorem.
- Newton on x³−3x+1
- Newton iteration for the reciprocal
- Cube root of 10 with Newton
- Newton exact for linear functions
- Classifying the discontinuity of the ratio of the absolute value of x to x
- Parameters for continuity and differentiability
- Zero of x³−3x+1 with bisection
- Function with no maximum on [0,1]
- Limit and discontinuity of the ratio of x to the absolute value of x