Week 3 Lab
Name_
Part 1: The Infinite Geometric Series
1. Given the following geometric series write out the first 5 partial sums. Explain how to do this.
4 ( 13 )
n
n=1
S1
S2
S3
S4
S5
=
=
=
=
2. Do these partial sums appear to be approaching a finite su

Week 3 Lab
Name_Chris Reyes_
Part 1: The Infinite Geometric Series
1. Given the following geometric series write out the first 5 partial sums. Explain how to do this.
4 ( 13 )
n
n=1
S1
S2
S3
S4
S5
= 4/243
= 4/81
= 4/27
= 4/9
= 4/3
In order to complete th

Week 1 Lab
Name_Chris Reyes_
2
Part I - Directions: For the function
f ( x )= ( x 2 )2+2 dx
we are going to estimate the area under
0
the curve using the trapezoidal rule where n = 5 by doing the following:
1. Divide the interval into 5 equal pieces. How

Week 2 Lab
Name_Christion Reyes_
Part 1: Rules for integrating trigonometric functions
sin
m
x cosn x dx
There are three rules governing how we deal with integrals of this form.
1. If the power of the sine is odd and positive, save one sine factor and
co

Week 7 Lab
Name_Chris Reyes_
Solve
y -5 y'-6 y= cfw_e ^ cfw_-2 t where y(0) = 1 and y(0) = -1 using LaPlace Transforms
1. Step 1: Rewrite the left side of the equation using the LaPlace substitutions for y, y, and y. See
either the week 7 lecture or page

Week 6 Lab
Name_Chris Reyes_
Part I: Second Order Homogeneous Differential Equations
1. What is meant by homogeneous? What should you look for to determine the order of a
differential equation?
A homogeneous differential equation only uses the y derivativ

Week 5 Lab
Name_Chris Reyes_
Part I: Separable Differential Equations
1. What is meant by separable? What should you look for in a differential equation to decide if it is
separable or not?
An equation will be separable when there are two different variab

Week 4 Lab
Name_Chris Reyes_
Part I: Taylor Series
Directions: Determine the Taylor Series for the following function:
a=1
1. Determine the first four derivatives of
f I ( x ) =
f II ( x )=
f III ( x )=
f IV ( x )=
f ( x )=ln ( x 2 ) for n = 4 where
f ( x