Math 130: Written Homework 2

Solution due Friday, Feb 10 Name:

Problem Statement (Examples Library)

Let f(x) be a function defined for all real numbers. Each of the statements below is true sometimes. For each of the statements below give an example of a function for which it holds true and an example of a function for which it does not hold true (this means you will have a total of 8 answers; 2 for each prompt). When appropriate, explain why your examples work.

1. limf(x)=f(3) x3

2. If lim f(x) = 1, then f(0) = 0. x0 x

3. If lim f(x) = a, then lim 1 = 1. (You may choose any a that you wish for your examples.) x7 x7 f(x) a

4. If lim f(x)>0and lim f(x)>0,then limf(x)>0. x5+ x5 x5