MTH 200 SL1 Weekly Check in Assignment 7 - Solution
1. Find the absolute maximum and absolute minimum values, if they exist, for
f ( x) x3 9 x 2 24 x 14 over the interval (-2, 3)
Since this is an open interval we need to find f(x) and f(x).
f ' ( x) 3x 2
Practice Exam 1 Applied Calculus
1. An investor deposits $2100 into an account that bears 3.2% interest where
the interest is compounded quarterly. How much will be in the account
after 6 years?
2. A manufacturer of radios has determined that the Supply f
Miguel Angel Martinez
03/23/2014
MTH200-SL1
Professor Mahar
Due: 03/29/2014
Weekly Check-In Assignment 9
a.
Write an equation that describes the number of stores open t years after bankruptcy.
a.
The court determines that the company will become profitabl
Miguel Angel Martinez
04/28/2014
MTH200-SL1
Professor Mahar
Due: 05/03/2014
Weekly Check-In Assignment 13
1.
A couple decides to deposit $1600 per year, in a continuous money flow, into an account that bears 8%
interest. What is the Accumulated Present Va
Miguel Angel Martinez
03/17/2014
MTH200-SL1
Professor Mahar
Weekly Check-In Assignment 8
Calculate the derivative of the following functions, do not simplify your answers.
1.
1.
Due: 03/22/2014
Miguel Angel Martinez
01/27/2014
MTH200-SL1
Professor Mahar
Due: 02/01/2014
Weekly Check-In Assignment 2
1. Find the equation of the line passing through (-2,6) and (3,-4) in slope-intercept form.
y=mx+b; m=y/x = (y2y1)/(x2 x1) = (4)6)/(3(2)= (10)/5=2;
6
Miguel Angel Martinez
02/25/2014
MTH200-SL1
Professor Mahar
Weekly Check-In Assignment 5
Differentiate the following. Do not simplify your answers.
1.
1.
Due: 03/01/2014
Miguel Angel Martinez
02/03/2014
MTH200-SL1
Professor Mahar
Due: 02/08/2014
Weekly Check-In Assignment 3
1.
1.
Determine the following limit algebraically, if it exists. If the limit does not exist explain why.
Miguel Angel Martinez
02/10/2014
MTH200-SL1
Professor Mahar
Due: 02/15/2014
Weekly Check-In Assignment 4
1.
Determine whether the given function is continuous at x = -2, if it is not continuous explain why.
Due to the fact that the function has a hole at
MTH 200 SL1 Weekly Check in Assignment 1 - Solution
1. Given f ( x) 2 x 2 4 x 5 and g ( x) 6 x 7 determine ( f g )( x)
( f g )( x) f ( g ( x) 2( g ( x) 2 4( g ( x) 5
2(6 x 7) 2 4(6 x 7) 5 2(36 x 2 84 x 49) 24 x 28 5
72 x 2 168 x 98 24 x 28 5 72 x 2 144
MTH 200 SL1 Weekly Check in Assignment 2
1. Find the equation of the line passing through (-2, 6) and (3, -4) in slope
intercept form.
6 (4) 10
2
23
5
y 4 2( x 3)
m
y 4 2 x 6
y 2 x 2
2. A manufacturer of radios has determined that the Supply function fo
MTH 200 SL1 Weekly Check in Assignment 13 Solution
1. A couple decides to deposit $1600 per year, in a continuous money flow, into an
account that bears 8% interest. What is the Accumulated Present Value of the account
after 18 years?
18
1600e
0
0.08t
dt
MTH 200 SL1 Weekly Check in Assignment 14 Solution
Given
f ( x, y, z) 3xy 4 ln(4 xz 2 ) 6 xyz 2 6 yz
Calculate the following:
f x , f y , f z , f xy , f zx
1
1
(4 z 2 ) 6 yz 2 0 3 y 4 6 yz 2
2
4 xz
x
f y 12 xy 3 0 6 xz 2 6 z
fx 3y4
1
2
(8 xz ) 12 xyz 6 y
MTH 200 SL1 Weekly Check in Assignment 15 Amnesty Week
Solution
f ( x) x3e(5 x
8
9 x 2)
1. Find f ' ( x) for
We need to use the product rule with the chain rule inside it.
f ' ( x) 3 x 2 e ( 5 x
8
9 x 2)
2. Evaluate the following integral:
x3e(5 x
5
2
(
Applied Calculus (MTH 200) Course Review
For 1-9, find each limit, if it exists:
1.
lim
x -5
x 2 25
x5
2.
6
lim
x -3 x 3
3.
lim
3 x h 2 3x 2
h0
h
x h 1 x 1
lim
2
4.
3
lim (3x - 4x + 2x + 3)
x 1
lim
Graph: f(x) =
c)
11.
a)
2
5.
lim (x + h)
h 0
8.
x 2 5x
MTH 200 SL1 Weekly Check in Assignment 12 Solution
Evaluate the following:
1.
(x e
2 2x
)dx
We need to do integration by parts on this (twice)
u x2
dv e 2 x dx
plugging these into the formula we get
1
du 2 xdx
v e2 x
2
1 2 2x
x e xe 2 x dx
2
We then need
MTH 200 SL1 Weekly Check in Assignment 10 - Solution
1. Approximate the area between the graph of f ( x) x3 8 and the x-axis over the
interval [3, 6] using 6 subintervals evaluated at the left hand endpoints.
63
1/ 2
6
f(3) = 19, f(3.5) = 34.875, f(4) =
MTH 200 SL1 Weekly Check in Assignment 3 - Solution
1. Determine the following limit algebraically, if it exists. If the limit does not exist explain
why.
lim
x 9
x 3
x9
Solution: When we plug 9 in we get a 0/0 limit, so we need to do some algebra. We nee
MTH 200 SL1 Weekly Check in Assignment 4 - Solution
1. Determine whether the given function is continuous at x = -2, if it is not continuous
x2 4
explain why. f ( x) x 2 , x 2
4, x 2
Using the Continuity Checklist: f(-2) = 4, so it exists.
x2 4
( x 2)(
MTH 200 SL1 Weekly Check in Assignment 5 - Solution
Note: You may (and are encouraged to) use any shortcut rules on
this and future assignments.
Differentiate the following. Do not simplify your answers.
1.
s(t ) (6t 3 2t 2 )3 (7t 4 6t 4)5
We need to use
MTH 200 SL1 Weekly Check in Assignment 9 - Solution
A company with 10,000 stores goes bankrupt and is forced to close stores at a rate of 8%
dN
0.08 N
dt
per year, continuously.
a. Write an equation that describes the number of stores open t years af
MTH 200 SL1 Weekly Check in Assignment 8 - Solution
Calculate the derivative of the following functions, do not simplify your answers.
1.
f ( x)
ln x
x3
We can use the Product Rule (after rewriting the function) of Quotient Rule. Using
3
the Quotient Rul