MA115 Mathematical Analysis I Test 1
Instructions The test consists of two sections, Part 1: Questions 1 6 Part 2: Questions 7 10 You are to do all of Part 1. For Part 2, select and complete 2 of the 4 problems given. Please clearly indicate which
Ma 116
Summary of Key Topics
Spring, 2007
Sections 4.5, 5.10 L'Hospital's Rule: Recognize indeterminate forms of the type 0/0, /, 0 ; Convert to 0/0 or / before applying L'Hospital's Rule; Then, lim f (x) f (x) = lim xa g (x) g(x) (if the limit o
MA 115 Quiz - Precalculus (September 11, 2008)
Show all work. Answers without supporting work will not receive credit.
1. Solve the following inequalities: [8pts]
a) |2 3x| 3
b) |3x 2| + 1 > 2
2. Find the domain for the following functions: [8pts]
a) f (x
1. [10]
2. [10]
3. [10]
4. [10]
5. [10]
6. [10]
Total
7. [10]
8. [10]
9. [10]
10. [10]
11. [10]
12. [10]
Total
Final Grade [120]:
MA115 - Final (December 18, 2009)
Show all work. Answers without supporting work will not receive credit.
No calculators or c
Ma 115
Exam 2
Nov 11, 2010
There are some formulas for area and volume on page 6.
1. [10 pts]
Compute the following derivatives. Assume b is a positive constant.
i) y(x) = 3x6 + 5/x
ii) h(t) =
4t
4+t
iii) g() = esin
iv) f (z) = (ln 3)z 2 + (ln 4)ez
v) g(
Ma 115
Quiz 2
1. [10 pts]
Oct 9, 2008
Evaluate f 0 (x) for the following functions. (Simplify your results when possible.)
(a) f (x) =
ex
x2 + 1
(b) f (x) = x 3
3
x+
x
2. [10 pts]
2
x x 2
x 6= 1
2x + 2
(a) Consider the function f (x) =
.
A
x = 1
If poss
Ma 115
Exam 1
Oct 7, 2010
1
1. [5 pts] For the function f (x) = , determine the derivative function f 0 (x) directly
x
from the definition of the derivative as a limit.
(No credit for applying formulas derived in Chapter 3.)
2. [5 pts] For the graph of y
Ma 115
Final Exam
1. [6 pts]
For the rational function, f (x) =
Dec 17, 2010
2x + 3
,
x+1
identify the domain of f ,
determine all roots of f ,
identify and describe all vertical and horizontal asymptotes of y = f (x).
2. [6 pts]
Evaluate the following
MA115 - Final (December 15, 2008)
Show all work. Answers without supporting work will not receive credit.
1. [10 pts]
(a) Give the precise definition of what it means for the function f ( x) to be continuous at the
point x a .
(b) Find the constants a and
C+ Basics - Part 1
1
C+ Basics
Integer data types In our first program the data type of the variables we have used is int. Thus we can store whole numbers in these variables. In this part, we will discuss: two other integer types long and short fo
MA 115 Homework Solutions for Week 8 5.7 #18 A B x-1 = + . Multiply both sides by (x + 1)(x + 2) to get x - 1 = A(x + 2) + B(x + 1). x2 + 3x + 2 x+1 x+2 Substituting -2 for x gives -3 = -B B = 3. Substituting -1 for x gives -2 = A. Thus,
1 0
x-1 dx
MA 115 Homework Solutions for Week 7 5.5 #10 xex dx =
2
Let u = x2 . Then du = 2x, so 5.5
1 2
1 eu ( 2 du) = 1 eu + C = 1 ex + C 2 2
2
#20
1 2 du, so
Let u = 2. Then du = 2d and d = sec 2 + C #22
sec 2 tan 2d =
sec u tan u( 1 du) = 2
1 2
sec
MA115 Mathematical Analysis I Test 2
Instructions The test consists of three sections, Part 1: Questions 1 6 Part 2: Questions 7 10 Part 3: Bonus Question You are to do all of Part 1. For Part 2, select and complete 2 of the 4 problems given. Plea
MA115 Mathematical Analysis I Test 3 Answer Key
Instructions The test consists of three sections, Part 1: Questions 1 6 Part 2: Questions 7 10 You are to do all of Part 1. For Part 2, select and complete 2 of the 4 problems given. Please clearly i
Ma 115 Homework Solutions for Week 2 2.2 #4
x0
(a) lim f (x) = 3 (c) lim f (x) = 2 +
x3
(b) lim f (x) = 4 -
x3
(d) lim f (x) does not exist because the limits in (b) and (c) are not equal.
x3
(e) f (3) = 3
2.2
xa
#6
lim f (x) exists for all a
MA 115 Homework Solutions for Week 3 2.7 #4
(a) Since g(5) = -3, the point (5, -3) is on the graph of g. Since g (5) = 4, the slope of the tangent line at x = 5 is 4. Using the point-slope form of a line gives us y - (-3) = 4(x - 5), or y = 4x - 23
MA 115 Homework Solutions for Week 4
3.5
#2 u = u1/2 .
Let u = g(x) = 4 + 3x and y = f (u) = Then
dy dx
=
dy du du dx
1 = 2 u-1/2 (3) =
3 2 u
=
3 . 2 4+3x
3.5
#6
Let u = g(x) = ex and y = f (u) = sin u. Then
dy dx
=
dy du du dx
= (co
MA 115 Homework Solutions for Week 5 4.2 #6
Absolute maximum value is f (8) = 5; absolute minimum value is f (2) = 0; local maximum values are f (1) = 2, f (4) = 4, and f (6) = 3; local minimum values are f (2) = 0, f (5) = 2, and f (7) = 1.
4.2
#
MA 115 Homework Solutions for Week 6 4.9 #12
x +x+1 1 = x + 1 + F (x) = f (x) = x x 4.9
2
1 2 2x 1 2 2x
+ x + ln |x| + C1 + x + ln |x| + C2
if x < 0 if x > 0
#19 f (x) = x(6 + 5x) = 6x1/2 + 5x3/2 f (x) = 4x3/2 + 2x5/2 + C f (1) = 6 + C
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3.[10]
MA115
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Total: [50]
Exam 3
Name:
Dec 9, 2010
MyStevens Username:
Check your lecture:
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