Find a power series representation for the function. (assume a > 0.) (give your power series representation centered at x = 0.) f(x) = x3 a6 − x6

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?

Organic apples are on special for $1.50 per pound. does total cost vary inversely or directly with the number of pounds purchased? find the cost of 3.4 pounds of apples. a. inversely: $5.10 b. directly; $5.10 c. inversely: $2.27 d. directly; $2.27

Which of the following exponential functions goes through the points (1, 6) and (2, 12)? f(x) = 3(2)x f(x) = 2(3)x f(x) = 3(2)−x f(x) = 2(3)−x