the pythagorean theorem
DESCRIPTION
The Pythagorean theorem. Algebra 1 CP. Warm up. Draw a right triangle. What characteristics do you know about it? Angles? Sides?. Right triangle Pythagorean theorem. Example 1. A right triangle has legs of lengths 9cm and 12cm. What is the length of the hypotenuse?. - PowerPoint PPT PresentationTRANSCRIPT
9-1 SequencesObjective: Determine whether a sequence
converges or diverges and use properties of monotonic sequences and bounded sequences.
Ms. BattagliaAP Calculus
a) The terms of the sequence {an} = {3 + (-1)n} are
b) The terms of the sequence {bn} = are
Listing the Terms of a Sequence
c) The terms of the sequence {cn} = are
d) The terms of the recursively defined sequence {dn}, where d1 = 25 and dn+1 = dn - 5
Listing the Terms of a Sequence
Find the limit of the sequence whose nth term is
Finding the Limit of a Sequence
a) {an} = {3 + (-1)n} b) {bn} =
Determining Converges or Divergence
Show that the sequence whose nth term is
convergence.
Using L’Hôpital’s Rule to Determine Convergence
Show that the sequence converges, and find its limit.
Using the Squeeze Theorem
Find a sequence {an} whose first five terms are
Finding the nth term of a Sequence
Determine an nth term for a sequence whose first five terms are
Finding the nth Term of a Sequence
Determine whether each sequence having the given nth term is monotonic.
a) b) c)
Determining Whether a Sequence is Monotonic
a. {an} = {1/n} b. {bn} = {n2/(n+1)} c. {cn}={(-1)n}
Bounded and Monotonic Sequences
Day 1: Read 9.1 Page 604 #45-51 odd, 85-95 odd
Day 2: Page 604 #55-67 odd, 88-99 even, 119-124
Classwork/Homework