four decimal places.
(c) Use the Limit Laws to find the exact value of the limit.
37. Use the Squeeze Theorem to show that
\(\lim_{x \to 0} x^2 \cos 20\pi x = 0\)
Illustrate by graphing the functions \(f(x) = -x^2\),
\(g(x) = x^2 \cos 20\pi x\), and \(h(x) = x^2\) on the same screen.
38. Use the Squeeze Theorem to show that
\(\lim_{x \to 0} \sqrt{x} + x^2 \sin \frac{\pi}{x} = 0\)
Illustrate by graphing the functions \(f\), \(g\), and \(h\) (in the nota-
tion of the Squeeze Theorem) on the same screen.
39. If \(4x - 9 \le f(x) \le x^2 - 4x + 7\) for \(x \ge 0\), find \(\lim_{x \to 4} f(x)\).
40. If \(2x \le g(x) \le x^2 + 2\) for all \(x\), evaluate \(\lim_{x \to 2} g(x)\).
