ETBU General Electric and the Hudson River Cleanup Analysis Paper Tom Kennedy MA 525 Hwk # 7 Question #1 Use the − δ definition to prove that f (x) = x4

ETBU General Electric and the Hudson River Cleanup Analysis Paper Tom Kennedy
MA 525
Hwk # 7
Question #1 Use the − δ definition to prove that f (x) = x4 is uniformly continous on (0,1).
(
x2 sin x( π2 ), x 6= 0
Question #2 Prove that f (x) =
is differentiable for all x ∈ R
0,
x=1
√
Question #3 Use Taylor’s Theorem with n = 2 to approximate 1.2 to within two decimal
places. Hint you should include
 the value of P2 (0.2) and a bound for the remainder R2 (0.2).

n, if 0 ≤ x < 1/n Question #4 let fn (x) = 0 if 1/n < x ≤ 1 for all nN.   0, if x = 0 (a) Show thazt fn → 0 pointwise on [0, 1] R1 (b) Show that the above convergence is not uniform. Hint compute 0 fn (x)dx. Question #6 If (an ) is a sequence and if lim(n2 an ) exists in R, show that convergent. i P an is absolutely Purchase answer to see full attachment