1. a) Explain the difficulty of computing f(x) for a small value of |x| and show how it can be circumvented.

b) Compute (condf f)(x) and discuss the conditioning of f(x) for small |x|.

c) How can the answers to (a) and (b) be reconciled?

Let f(x) = √ (1 + x)^4 − 1

2. Explain how to evaluate the following functions accurately for small x (i.e., |x| ≈ 0). Show how to mitigate cancellation error and compute the condition number:

a) 1 /(1 + 2x) − 1 − x/ 1 + x

b) √ (1/ x + x) − √ (1/ x - x)