Ch. 3 Basics about sequences and limits

Question 1

Definition of a bounded sequence xn

Answer 1

There exists a C > 0 such that |xn| ≤ C for all n ∈ natural numbers

Question 2

State the squeezing theorem

Answer 2

If |xn| ≤ |yn| for all n in the natural numbers and yn –>0 as n –> infinity, then also xn –> 0 as n –> infinity

Question 3

Sate COLT

Answer 3

Let x* be limit n–>∞ (xn) and y* be limit n–> ∞ (yn), let a,b be constants, then:

(i) axn + byn –> ax* + by* as n–> ∞
(ii) xnyn –> xy as n–> ∞
(iii) xn/yn –> x/y as n–> ∞

Question 4

Definition of e

Answer 4

lim n–>∞ (1 + 1/n)^n

Question 5

Facts about limits

Answer 5

Exponentials beat powers

Powers beat logarithms

Question 6

Modulus of a + ib

Answer 6

sqrt(a^2 + b^2)