HW 2 worksheet. Due Wed Feb 5, 2008.

Bartle: Section 11.4 p. 333 #2, 3.

Consider the two metrics d₁ and d_infinity on C[0,1]. Give an example of two functions in C[0,1] whose distance is small in one metric yet large in the other.

The function f(x) identically zero is called the zero function. Define a sequence of functions f_n(x) such that the sequence converges to the zero function in both the d₁ metric and d_infinity metrics. Prove the convergence using the definition of limit in a metric space.