Suppose an and bn are series with positive terms and bn is known to be convergent. (a) if an > bn for all n, what can you say about an ? why? an diverges by the comparison test. an converges if and only if an ≤ 2bn. an converges if and only if an ≤ 4bn. an converges by the comparison test. we cannot say anything about an . (b) if an < bn for all n, what can you say about an ? why? an converges if and only if bn 4 ≤ an ≤ bn.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0