Assignment:
Q1. Suppose f: [a,b] → P is a function such that f(x)=0 for every x ∈ (a,b].
a) Let ε > 0. Choose n ∈ N such that a + 1/n < b and |f(a)|/n < ε.
Let P ={a, a+1/n, b} ε π([a,b]). Compute Y (f,P) - Λ(f,P) and show that is less than ε.
b) Prove that ∫ab f = 0.
Provide complete and step by step solution for the question and show calculations and use formulas.