Alice and bob are arguing over their results from soft analysis. you will find who is right by hard analysis. in other words, find an input error ? > 0 small enough such that the output error e iclaim- truel 1. true lim 8 a. claim: lim x39 x? 2 2. true lim a. claim: lim|=1 4 x- 3 write the definition of a derivative in terms of s and 6

The base of a triangle exceeds the height by 7 centimeters. if the area is 400 square centimeters, find the length of the base and the height of the triangle.

The number of branches on a tree demonstrates the fibonacci sequence. how many branches would there be on the next two levels of this tree? 13 | | | m branches

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?