MATLAB PROJECT 1
Please read the Instructions located on the Assignments page prior
to working on the Project.
Failure to fulfill the requirements on the format will result in a loss of
points.
BEGIN with creating a diary file Project1.
Note: All exercise
MAS 3114 (Web)
SUMMER 2017
SYLLABUS
COURSE TITLE:
Computational Linear Algebra
CATALOG DESCRIPTION:
Linear equations, matrices, and determinants; vector
spaces and linear transformations; inner products and eigenvalues. This course emphasizes
computationa
MATLAB PROJECT 3
Failure to fulfill the requirements on the format will result in a loss of
points.
BEGIN with creating a diary file Project3.
Note: All exercises in this project will be placed in this diary file. Each exercise in the diary
file should be
Calculus I
Review : Functions
2
1. Perform the indicated function evaluations for f ( x ) =3 5 x 2 x .
(a) f ( 4 )
(b) f ( 0 )
(c) f ( 3)
(d) f ( 6 t )
(e) f ( 7 4 x )
(f) f ( x + h )
(a) f ( 4 ) [Solution]
f ( 4) =
3 5 ( 4) 2 ( 4) =
49
2
(b) f ( 0 ) [Sol
Calculus I
g=
(t + h)
t+h
t+h
=
2 ( t + h ) + 6 2t + 2h + 6
Hint : Dont let the fact that there are now variables here instead of numbers get you confused.
This works exactly the same way as the first three it will just have a little more algebra involved
Calculus I
R ( x + 1) =
3 + ( x + 1)
4
=
( x + 1) + 1
4+ x
4
x+2
Hint : Dont let the fact that there are now variables here instead of numbers get you confused.
This works exactly the same way as the first three it will just have a little more algebra i
Calculus I
Step 3
f ( t + h ) f ( t ) 4th + 2h 2 3h
=
= 4t + 2h 3
h
h
8. The difference quotient of a function f ( x ) is defined to be,
f ( x + h) f ( x)
h
1
compute the difference quotient for y ( z ) =
.
z+2
Hint : Dont get excited about the fact that
Calculus I
(f) f ( x + h ) [Solution]
f ( x + h ) =3 5 ( x + h ) 2 ( x + h )
2
=3 5 ( x + h ) 2 ( x 2 + 2 xh + h 2 )
=3 5 x 5h 2 x 2 4 xh 2h 2
(b) g ( 3)
t
.
2t + 6
(c) g (10 )
(e) g ( t + h )
(f) g t 2 3t + 1
2. Perform the indicated function evaluations
A little AP Preparation
[No Calculator] There are 700 people in line for a popular amusementpark ride when the ride begins operation in the
morning. Once it begins operation, the ride accepts passengers until the park closes 8 hours later. While there is
5. Let R be the region in the rst quadrant enclosed by the graphs of yl= 2x and y2= x2 , as shown below.
a) Find the area ofR. Ask : < (5 (cfw_J a) ' Ll):
J0 xmx =2 gave?
3
=( Elwt") =% e
b) The region R is the base of a solid. For this solid, at [email protected] cro
A little AP Preparation
b\"Calculator] The rate at which people enter an auditorium for a rock concert is modeled by the mction R given by
R (t) : 1380t2 675i3 for 0 5 t g 2 hours; R (t) is measured people per hour No one is in the auditorium at time t =
AP Calculus l
7.1 Worksheet ; 69% dd?
All work must be Shown in this course for full credit. Unsupported answers may receive NO credit.
1. Fill in the blanks.
a) Integrating velocity gives d cfw_5! mfg mg nj, ( (Wt ('14 90311519
b) Integrating the absolut
AP Calculus Co 9461
7.3 Worksheet (Day 2)"
>/\All work must be shown in this course for dl credit. Unsupported answers may receive N0 credit
1. Suppose region R is in the rst quadrant bounded by the graphs of y = cfw_/Jc and x = 8.
a) If R is rotated abou
AP Calculus & 09d 6
7.3 Worksheet (day 3)
All work must be shown in this course for full credit. Unsupported answers may recezveNO credit.
1. Let R be the region between the graphs of y = l and y = sin x from x = 0 to x = 3 . What isthe volume of the soli
5. Tickets to a concert were sold out in 24 hours. The graph below shows th.t which people bought tickets to the concert
during the 24hour period. Before the tickets went on sale, 100 tickets had been set aside for VIPs.
a) How does the graph indicate th
4. Let R be the region in the rst quadrant bounded by the graph of y = 2J3; ,
the horizontal line y = 6, and the y-axis, as shown in the gure above.
A. 6]
a) Findthe areaofR. iii/Z, : [(0 -0?~l:> Ax
b) Write, but do not evaluate, an integral expression
4. [Calculator] Let R be the region enclosed by the graphs of y 2 111(3:2 +1) and y = cos x.
21) Find the area of R.
E /
lamag : f 003x Vin (x2+l\ olx
A
/ (
\Aakhlxt'i'b 7 Q30 we
, _ \ ./
P; Austen? Amie : I. [57354014 @355, i q
A e g , 30' P"
E. Solutions to 18.01 Exercises
1. Dierentiation
c) undened (both are possible)
d) Note that 2 x is negative when x > 2, so the limit is
e) Note that 2 x is positive when x < 2, so the limit is + (can also be
written )
f)
4x2
4x
=
= as x
x2
1 (2/x)
1
g)
Codl
AP Calculus
7.2 Worksheet
All work must be shown in this course for full credit. Unsupported answers may receive NO credit.
1. Find the area of the shaded region analytically (without a calculator).
17/s
a) y = 0.55%2 (x) Pram: ] [0'59 K '('43M
E. Solutions to 18.01 Exercises
1. Dierentiation
h) (xx ) = ex ln x = (x ln x) ex ln x = (ln x + 1)ex ln x = (1 + ln x)xx
i) (ex ex )/2
j) (ex + ex )/2
k) 1/x
l) 1/x(ln x)2
m) 2ex /(1 +
x 2
e )
1
(even)
1I-3 a) As n , h = 1/n 0.
1
ln(1 + h)
ln(1 + h) ln(1
7. [No Calculator] The region bounded below by the parabola y =- x2 and above by the line y = 4 is to be
partitioned int two subsections of emu rea y cutting across it with the horizontal line y = c.
a) Sketch the regio and draw a line y = c across it tha
AP Calculus t 1
7.3 Worksheet (Day 1) a 0 Ll chi
All work must be shown in this course for full credit. Unsupported answers may receive N 0 credit.
1. [No Calculator] Theaase of a solid is the region enclosed by the graph of y = e" , the coordinate axes,
E. Solutions to 18.01 Exercises
1. Dierentiation
c)
h(t) h(5)
400 16t2 0
16(5 t)(5 + t)
=
=
t5
t5
t5
= 16(5 + t) 160ft/sec as t 5
(5)
(6)
1B-2 A tennis ball bounces so that its initial speed straight upwards is b feet per
second. Its height s in feet a
1. Dierentiation
E. Solutions to 18.01 Exercises
with c1 = cos() and c2 = sin().
1J-4 a) The Pythagorean theorem implies that
c2 = sin2 + (1 cos )2 = sin2 + 1 2 cos + cos2 = 2 2 cos
Thus,
c=
2 2 cos = 2
1 cos
= 2 sin(/2)
2
b) Each angle is = 2/n, so the
SOLUTIONS TO 18.01 EXERCISES
Unit 1. Dierentiation
1A. Graphing
1A-1,2 a) y = (x 1)2 2
b) y = 3(x2 + 2x) + 2 = 3(x + 1)2 1
2
2
1
1
-2
1b
1a
1A-3 a) f (x) =
1
-2
-1
2a
2b
(x)3 3x
x3 3x
=
= f (x), so it is odd.
1 (x)4
1 x4
b) (sin(x)2 = (sin x)2 , so it is
4.03 Context and Connotation
Hoped - Text: had long hoped to cover Definition - want something to happen or be the case.
Dream - Text: finds himself on the big screen Definition - a series of thoughts, images, and
sensations occurring in a person's mind d
Module 7 DBA
7.01
A right triangle has two legs and a hypotenuse
Hypotenuse - the longest side of a right triangle, opposite the right angle.
The trigonometric functions (also called circular functions) are functions of an angle. They are
used to relate t
Peter The Great & King Charles I
Empire
- Peter The Great - Rules the Tsardom of Russia and later the Russian
- King Charles - Was the monarch of the three kingdoms of England,
Scotland, and Ireland
In Depth Of The Two Rulers
Peter The Great had a major i