Math1012
Spring 2007
IIB-1
Consider the differential equation y' = x y
Draw the direction field for this
differential equation at the nine points:
(0,0), (0, 1), (0, 2)
(1,0), (1, 1), (1, 2)
(2,0), (2, 1), (2, 2)
Sketch the solution that goes
Through the
Math1012
Spring 2003 Prelim
II-A1
Approximate the following integral using the Trapezoid Rule with n=2
4
0
x 3 3x + 7 dx
Estimate the error
K (b a )3
| Et |
; | f '(x ) | K ; a x b
2
12n
Math1012
Spring 2003 Prelim
A1
Approximate the following integral us
Math1012
Fall 2004
I-B1
The region enclosed by the x-axis and the curve y = x
x is rotated about an axis specified below. Set up, but
do not evaluate and integral that comprises the volume
generated by rotating the region about
The y axis
The line y = 1
Math1012
Fall 2006/2008
Find g'(2), where g(x) =
x2
I-A1
3x
1
e sint
dt
2
1 +t
If F (x ) = x sintdt , find F'(
0
2
)
Math1012
Fall 2006/2008
A1
Find g'(2), where g(x) =
3x
g'(x) =
d
dx
g'(x) =
e sin(3 x ) d
1 +(3x )2 dx
g'(x) =
e sin(3 x )
1 +(3x )2
=
g'(
Math1012 Series Review
Nth Term Test
if lim an 0 or lim an DNE, then
n
n
a
diverges
n
Geometric Series Test
n
a (r )
if | r |< 1, then a
n
if | r | 1, then a
n
converges to
n
diverges to
=0
a
1-r
Telescoping Test
Write out the terms of the series and s
Chipotle Business Case Study
1
Chipotle Business Case Study
Javkhlantugs Altansukh
Lindenwood University
Chipotle Business Case Study
2
Introduction
Like many other entrepreneurs Steve Ells founder of Chipotle opened his first restaurant
in 1993 with grea