Try It Now
Work these exercises to see how well you understand this material.
Exercises
- By the recursive definition of binomial coefficients,
. Continue expanding
to express it in terms of quantities defined by the basis. Check your result by applying the factorial definition of
.
- Let p(x) = x5 + 3x4− 15x3 + x − 10.
- Write p(x) in telescoping form.
- Use a calculator to compute p(3) using the original form of p(x).
- Use a calculator to compute p(3) using the telescoping form of p(x).
- Compare your speed in parts b and c.
- What is wrong with the following definition of f : ℝ → ℝ? f (0) = 1 and f(x) = f(x/2)/2 if x ≠ 0.
Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/ads-latex/ads.pdf This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.