Quiz
F0 A
Name: A537
Honor Code: On my honor, I have neither received nor given any aid during this examination.
Signature:
1. (2 points). Multiple Choice question. If f and g are diifenrentiable functions such that
f(1) = 2: fl(]') = 3: f(2) =
9(1) = 2:
Math 161
Homework 5 Solutions
Summer 2015
Drew Armstrong
Book Problems:
Chap
Chap
Chap
Chap
Chap
4.5
5.2
5.4
5.6
6.1
Exercises
Exercises
Exercises
Exercises
Exercises
2, 8, 14
16, 20, 56
42, 44, 46
8, 16
2, 14, 30
Additional Problems:
A1. Let r > 0 be con
Math 161
Homework 3 Solutions
Summer 2015
Drew Armstrong
Book Problems:
Chap
Chap
Chap
Chap
2.5
2.8
3.3
3.5
Exercises
Exercises
Exercises
Exercises
8, 22, 24, 38
11, 12, 22, 24
22, 34
2, 4
Solutions:
2.5.8. Let y = (4x x2 )100 . Compute
dy
dx .
Well use t
Math 161
Homework 2 Solutions
Summer 2015
Drew Armstrong
Book Problems:
Chap 2.1 Exercises 4, 14, 18
Chap 2.2 Exercises 4, 6, 7
Chap 2.3 Exercises 2, 4, 8, 16, 20
Additional Problems:
A1. Recall that the number e is dened by the limit
e := lim
n
1+
1
n
Math 161
Homework 1 Solutions
Summer 2015
Drew Armstrong
1. Let Pn be a regular polygon with n sides and let C be the largest circle contained inside
Pn . Suppose that C has radius r.
(a) Compute an exact formula for the perimeter of Pn .
(b) Compute an e
Math 161
Homework 5
Summer 2015
Drew Armstrong
Book Problems:
Chap
Chap
Chap
Chap
Chap
4.5
5.2
5.4
5.6
6.1
Exercises
Exercises
Exercises
Exercises
Exercises
2, 8, 14
16, 20, 56
42, 44, 46
8, 16
2, 14, 30
Additional Problems:
A1. Let r > 0 be constant. In
Math 161
Homework 2
Summer 2015
Drew Armstrong
Book Problems:
Chap 2.1 Exercises 4, 14, 18
Chap 2.2 Exercises 4, 6, 7
Chap 2.3 Exercises 2, 4, 8, 16, 20
Additional Problems:
A1. Recall that the number e is dened by the limit
1 n
.
n
n
In class we inter
Math 161
Homework 4 Solutions
Summer 2015
Drew Armstrong
Book Problems:
Chap
Chap
Chap
Chap
Chap
3.7
4.1
4.2
4.3
4.4
Exercises
Exercises
Exercises
Exercises
Exercises
2, 4, 14
6
30, 38, 42
2, 6, 10, 14
6, 10
Solutions:
3.7.2. Find the most general antider
MTH 161
Algebra and Geometry Facts and Formulas
Algebraic fractions
a b
a b
cannot be simplified
b a
1
a b
a b a b
c
c c
Absolute value (assume a>0)
x a x a
x a x a or x a
x a axa
Inequalities (assume a>0)
x 2 a x a
x a x a or x a
x a axa
Proportionali
MTH 161/162N. Agras
Trig Facts and Formulas
Definitions and Special Angles/Triangles
Useful Pythagorean Triples:
Right Triangle Trig:
sin A
3, 4, 5
5, 12, 13
opposite
hypotenuse
cos A
7, 24, 25
adjacent
hypotenuse
tan A
8, 15, 17
opposite
adjacent
Trig
Quiz 2
FORM A
Name;
Honor Code: On my honor, I have neither received nor given any aid during this examinat 11.
Signature:
1. (3 points). Multiple Choice question. If f(x) = (1 + cosm)s1na: then f (7;) =
f (X): 8m LX + :4? cfw_Jiitv a
m
C)
(A
X
\Cf ' 3 r
Quiz 4
FORM A
Name: _i<_J<a3_.
Honor Code: On my honor, I have neither received nor given any aid during this examination.
Signature:
1. (3 points). Multiple Choice question. If 3:3 + 3mg + 293 = 17, then 2;: :
5x26? +3x43t 4. 6% air. -.- 0
6X X
_ z '
Quiz 1'; FORM A
Name. Belg,
Honor Code: On my honor, I have neither received nor given any aid during this examination.
Signature: _
1. (2 points). Multiple Choice question. Evaluate the limit.
\
limxcscm : W 7L 2.
:c>O r
Answer: _
2. (3 points). Mu
MTH 161 Fall 2016 N. Agras
1.
a.
b.
Review 3
Find the critical numbers for each of the following functions
3
2
f ( x) 2 x 5 3x 1
f ( x) x 3 x
2
3
2.
Find the absolute maximum and minimum values of the function on the given
interval.
y sin 2 x cos x
a.
Max
MTH 161 N. Agras Fall 2016 Review 2
1- Sketch the graph of the derivative function for each function whose graph is below
. i;
t ill. '
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MTH 161 N. Agras Fall 2016
Review 2
1.
Sketch the graph of the derivative function for each function whose graph is below.
2.
Determine the values of x where the function graphed below is not differentiable
3.
For each of the following functions, determin
MTH161N.Agras Exam2A Fall 2016
On my honor, I have neither given nor received any assistance on this examination.
Signature
Directions: Show your work neatly in the space provided. You MUST use a pencil. Exams in ink will not
be graded and will earn grade
W0 90 T
MTH 16] N. Agras Fall,2016 EXAM 1A SOLw cfw_O M
Pencil only. No graphing calculators PRINT LAST, First Name section
HONOR CODE. On my honor, I have neither given nor received any aid on this examination.
Signatule:
1-4: Evaluate the desired
Math 161
Homework 1
Summer 2015
Drew Armstrong
1. Let Pn be a regular polygon with n sides and let C be the largest circle contained inside
Pn . Suppose that C has radius r.
(a) Compute an exact formula for the perimeter of Pn .
(b) Compute an exact formu
Math 161
Quiz 2
Summer 2015
Drew Armstrong
No calculators are allowed on this quiz.
1. Let f (x) be a function. State the denition of the derivative function f (x). [Hint: No
words are necessary, just use symbols.]
There are many equivalent ways to state
Math 161
Quiz 3
Summer 2015
Drew Armstrong
1
Problems 1 and 2 refer to the function f (x) = x3 x.
3
1. [3 points] Compute f (x) and show that f (x) = 0 when x = 1 or x = +1. Determine
when f (x) is increasing or decreasing.
We have
1
f (x) = 3x2 1 = x2 1
Math 161
Quiz 5
Summer 2015
Drew Armstrong
Each problem is worth 2 points.
1. Compute the derivative of f (x) = x2 + 2x .
f (x) = (x2 ) + (2x ) = 2x + ln(2) 2x .
2. Use integration by parts to compute the most general antiderivative of g(x) = x ln(x).
Let
Math 161
Quiz 4
Summer 2015
Drew Armstrong
Each problem is worth 2 points.
1. Compute the most general antiderivative of f (x) = x2 2x + 3.
Using the power rule
xp dx =
1
p+1
p+1 x
x2 dx 2
f (x) dx =
(when p = 1) gives
x dx + 3
1
1
1 dx = x3 2 x2 + 3x + C
Math 161
Quiz 1
Summer 2015
Drew Armstrong
Compute the following limits, or say why they do not exist.
x2 4
x1 x 2
1. lim
Here we can just plug in x = 1 to get
x2 4
12 4
3
=
=
= 3.
x1 x 2
12
1
lim
x2 4
x2 x 2
2. lim
Here the limit has indeterminate form 0
Fall 2016
ENG 105
Hospital-Medina
Paper 3 Prompt
An In Depth Evaluation (Chapter 14 of Allyn & Bacon)
For Essay 3, you will be performing an evaluation. You may choose from the options below, or
choose your own topic with my approval. Regardless of what y
OXIRS/aou
MTH 161 Fall 2016 N. Agras Unit 1. Functions Review and Limits
A. Review of functions
Definitions: function, domain, range, increasing/decreasing/constant, independent/dependent variables
PVVu/hww A Whom $1ka C5Sl7ws +0 ecu/k lmWwtw do lm-1F 2,2
Oct/owlaow
MTH 161 N. Agras Fall 2016 Continuity; Limits at Infinity; Asymptotes
Definition of limit: limf(x) = L informally means that as x approaches the value x = c, f(x)
x->c '
approaches the value L
The formal definition of this expression is illustr
7: gaXUbhi) ; Sis/bx . 9029) BiWX 96.3%4 Oqlo/RDN
1 _.
/- V\ _ i I 4] in i
cfw_ WWW)?" W) ()0 =3
i MTH 161 N. Agras Fall 2016 Computing Derivatives , C 1 N .2 in . m 1,)
1- Real K ">'
i Review of Limits; Limits and Derivatives of f (t) = sint f (
I k awe-M reel; 4' ohm/1:34, = Mom-t- (52 palms) . wa [Roma
4: MalawiMm: my: Jr alumnae = Huggni- (uvwahVE)
MTH 161 F 2016 N. Agras Tangent Lines and the Definition of the Derivative
f'(x), the derivative of a function y = f(x) , is defined to be the limi