Chapter 2.2, Problem 49E

(a) Evaluate the function f(x) = x² – (2^x/1000) for x = 1, 0.8, 0.6, 0.4, 0.2, 0. 1, and 0.05, and guess the value of

$\underset{x\to 0}{\lim }\left(x^2-\frac{2^x}{1000}\right)$

(b) Evaluate f(x) for x = 0.04, 0.02, 0.01, 0.005, 0.003, and 0.001. Guess again.