4.5. Introduction to Taylor Series
4.5
CHAPTER 4. Sequences and Series
Introduction to Taylor Series
Given a function f (x) that can be represented by a power series
an (x a)n
f (x) =
n=0
centered at x = a, we have seen that f (x) has derivatives of all o
Precalculus
Exam 3
Sections 5.1-5.4,1.8
Show all work in order to receive credit.
Simplify all answers unless instructed otherwise.
1. (11 pts) Look at the parabola f (x) = 2x2
4x + 8
(a) Find all intercepts. Be sure to list all intercepts as points.
(b)
Precalculus
Exam 3
Sections 5.1-5.4,1.8,1.2
Show all work in order to receive credit.
Simplify all answers unless instructed otherwise.
1. (11 pts) Look at the parabola f (x) = 2x2
4x + 8
(a) Find all intercepts. Be sure to list all intercepts as points.
Review- Exam 3
Sections 5.1-5.4, 2.2,1.8
This is not an all inclusive list. just practice problems! Be sure to do some
exponential growth and decay ones too!
1. Find the vertex and all intercepts of the following parabolas
(a) x2
8x + 5
(x
x
y
2
4)
V = (4
Precalculus
Exam 1
Unless otherwise noted, you must show all work and simplify
answers to earn credit.
1. (6 pts) Find the length of an arc with angle 450 in a circle with radius 2
miles.
2. (10 pts) Suppose that tan =
other 5 trig functions.
4
3
and
<
<
Exam 2 Review
Sections 4.6-4.8, 2.3-2.5
This is not an all inclusive list. just a few basic practice problems!
1. Find the values of all of the trig functions when csc t = 2 and 32
t
p
2
csc t = 2 = H or sin t = 21 cos t = 23 sec t = p3 tan t =
1
O
p
3
co
Precalculus
Exam 2
Sections 4.5-4.8, 2.3-2.5
ceive credit.
Show all work in order to reSimplify all answers unless instructed
otherwise.
1. (6 pts) Sketch the graph of the reciprocal of the following function:
2. (16 pts) Fill out the blanks in the follow
Exam 1 Review
This list is not all inclusive! This is just one set of practice problems!
1. Describe the symmetry and nd the intercepts of
p
none
(0; 0)
(a) y = x
(b) y =
3x2
y
(c) y = jxj
axis only
y
axis only
2
2
(d) x + (y 3) = 10
( 1; 0), (1; 0)
(e) y
Precalculus
Exam 1
Unless otherwise noted, you must show all work and simplify
answers to earn credit.
1. (6 pts) Find the length of an arc with angle 450 in a circle with radius 2
miles.
=
s = r = (2miles)
4
2
2. (10 pts) Suppose that tan =
other 5 trig
Precalculus
Exam 2
Sections 4.5-4.8, 2.3-2.5
ceive credit.
Show all work in order to reSimplify all answers unless instructed
otherwise.
1. (6 pts) Sketch the graph of the reciprocal of the following function:
2. (16 pts) Fill out the blanks in the follow