Let f be defined on an interval 1. Suppose that there exists m > 0 and a> 0 such that: |f(x) – f(y)| < m|x – y|ª for all x, y E I (Such a function is said to satisfy a Lipschitz condition of order a on I. c) Show by example that a=1, then f is not necessarily differentiable on I.

2. Let f: I R be a continuous function on a bounded, closed interval I= [a, b). Show that f has a minimum on I.

How large should n be to guarantee that the Trapezoidal Rule approximation to x - 12x- 48x² + 2x + 5) dæ is accurate to within 0.1. n = How large should n be to guarantee that the Simpsons Rule approximation to 2 1(-a - 12a - 48z? + 2x + 5) dx is accurate to within 0.1. n = Hint: Remember your answers should be a whole numbers, and Simpson's Rule requires even values for n Question Help: Video 1 D Video 2 Submit Question P Type here to search hp

Let f: X→ Y and g: Y→ V be functions. Show the following: 3h : Y→ X such that ho f = idx (a) f is injective (b) f is surjective 3h: Y→ X such that foh = idy