REVISED_calc_wApps.qxd
6/21/05
1:55 PM
Page 1
Applied Calculus Review
Exponential Functions
Limits
x
Exponential Functions are functions of the form f (x) = a ,
where a 7 0, and a Z 1.
Linear Functions
for x first, and then substitute that number into the

REVISED_calc_wApps.qxd
6/21/05
1:55 PM
Page 2
Applied Calculus Review
Higher Derivatives
Related Rates
2
Notation: 2 Derivative: f (x),
nd
3rd Derivative: f (x),
1.
2.
3.
d y
, D 2 ( f (x), y
x
2
dx
d 3y
, D 3 ( f (x), y
x
3
dx
th
For derivatives 4 , the

REVISED_calc_wApps.qxd
6/21/05
1:55 PM
Page 2
Applied Calculus Review
Higher Derivatives
Related Rates
2
Notation: 2 Derivative: f (x),
nd
3rd Derivative: f (x),
1.
2.
3.
d y
, D 2 ( f (x), y
x
2
dx
d 3y
, D 3 ( f (x), y
x
3
dx
th
For derivatives 4 , the

Q SCI 291
Rules for Differentiating Functions Weeks 7 & 8
1. General Power Rule: If u(x) is a differentiable function and n is any real number
and y = f(x) = [u(x)]n, then dy/dx = n[u(x)]n-1 u(x), or dun/dx = nun-1 du/dx, where u =
u(x) (p. 235).
2. Chain

Q SCI 291
Rules for Differentiating Functions Weeks 5 & 6
1. Four-step process for differentiating functions using limits (p. 172).
2. Constant Function Rule: If y = f(x) = k, then dy/dx = 0 (p. 179).
3. Power Function Rule: If y = xp, then dy/dx = pxp-1

Q SCI 291
February 14, 2014
Dr. Bare
Hourly Examination Three
Name_key_
Closed book. May use calculator and applied calculus review card. Show all work for full
credit. This means show (if appropriate) which text book formula is used; plug in a few
repres

Q SCI 291
January 17, 2014
Dr. Bare
Hourly Examination One
Name_key_
Closed book. May use calculator and applied calculus review card. Show all work
for full credit. This means show (if appropriate) which text book formula is used;
plug in a few represent

Q SCI 291
January 31, 2014
Dr. Bare
Hourly Examination Two
Name_key_
Closed book. May use calculator and applied calculus review card. Show all work
for full credit. This means show (if appropriate) which text book formula is used;
plug in a few represent

Q SCI 291
Application Problem Answers from our Text for Weeks 3 and 4
Problem 56, page 105
Solve: I = 100e-.00942d
For d= 50 ft., I= 62.44%
for d=100 ft., I = 38.98%
Problem 58, page 105
The equation is: N=83e.032t with t=0 representing 2008. In 2020 (t=1

REVISED_calc_wApps.qxd
6/21/05
1:55 PM
Page 1
Applied Calculus Review
Exponential Functions
Limits
x
Exponential Functions are functions of the form f (x) = a ,
where a 7 0, and a Z 1.
Linear Functions
for x first, and then substitute that number into the

REVISED_calc_wApps.qxd
6/21/05
1:55 PM
Page 1
Applied Calculus Review
Exponential Functions
Limits
x
Exponential Functions are functions of the form f (x) = a ,
where a 7 0, and a Z 1.
Linear Functions
for x first, and then substitute that number into the

REVISED_calc_wApps.qxd
6/21/05
1:55 PM
Page 2
Applied Calculus Review
Higher Derivatives
Related Rates
2
Notation: 2 Derivative: f (x),
nd
3rd Derivative: f (x),
1.
2.
3.
d y
, D 2 ( f (x), y
x
2
dx
d 3y
, D 3 ( f (x), y
x
3
dx
th
For derivatives 4 , the