6) Assume that lim an = 5 and lim on = 0. n -too a) Then lim an = 0. b) Then lim an = 00. c) This is impossible if lim on = 0. n-+0o d) None of the above. 7) Assume that {an} satisfies a1 = 1 and anti = 1 + . If this sequence converges to L then, by the arithmetic rules for sequences L = lim an+1 = 1 + lim an 1 As such, which of these statements is the most appropriate in establishing the limit of {an }: a) L = 1+7. b) L = 1 + } provided that L # 0 . c) L = 1+ , since we can show by induction that an 2 1 for all n and hence L 0. 18) In the proof that if lim an = L and lim on = M, then lim an + on = L + M, a key tool was n-+0c 1 -+ 0o a) the Triangle Inequality. b) that convergent sequences are bounded. c) that | can - CL K E #| an - LKE d) All of the above. 19) In the proof that if lim an = L and lim bn = M, then lim an . bn = L . M, a key tool was n-too n -too a) the Triangle Inequality. b) that convergent sequences are bounded. c) that | can - CL K E # | an - L KE. d) All of the above