MATH 131-03, Fall, 2013
Quiz 11(a)
Name: _Solutions_
No Calculator. Show your work in details.
1. (3pts)
(a) Let fx 1 x .
(1) Find the linear approximation Lx at a 0.
1
f0 1 1, f x
, f 0 1
2
2 1x
Lx 1 1 x 0 1 x 1
2
2
(2) Use the linear approximation Lx o
MATH 131-03, Fall, 2013
Quiz 12
Name: _Solutions_
No Calculator. Show your work in details.
1. (3pts)
4 x 2 if 2 x 0
(a) Let fx
2x 1 if 0 x 2
.
(1) Sketch the graph of fx. Label your scales.
y4
(2) Give the following if it exists:
Local maximum value f2
MATH 131-03, Fall, 2013
Quiz 9
Name: _Solutions_
No Calculator. Show your work in details.
1. (6pts) Find the derivatives.
(1) hx 3 sin3x 2 x sin3x 2 x 1/3
h x
1
3
sin3x 2 x 2/3 3 cos3x 2 x ln2
x 1 4
x 2 2x 5
4x 1 3 1x 2 2x 5 x 1 4 5x 2 2x 4 2x 2
h x
2
MATH 131-03, Fall, 2013
Quiz 10
Name: _Solutions_
No Calculator. Show your work in details.
1. (6pts) Find the derivatives.
(1) hx = 2 sin3 lnx
h x = 2 cos3 lnx 3 1 = 6 1 cos3 lnx
x
x
(2) hx = ln x 2 1 x 2
h x =
x2
1
1 x2
2x 1 x 2 + x 2
2x
2 1 x2
=
1
x 1
Math 131 - Fall, 2010 Homework 1 - Due Friday, Aug. 27 Name: _Solutions_
Mathematics Quote: The pleasure we obtain from music comes from counting, but counting
unconsciously. Music is nothing but unconscious arithmetic. Gottfried Wilhelm Leibniz (1646-171
Math 131 - Fall, 2010 Homework 3 - Due Friday, Sept. 3 Name: _Solutions_
Mathematics Quote: But Nature flies from the infinite, for the infinite is unending or imperfect, and
Nature ever seeks an end. - Aristotle (384-322 B. C. E)
Instructions for homewor
Math 131 - Fall, 2010 Homework 2 - Due Tuesday, Aug. 31 Name: _Solutions_
Instructions for homework:
(1) Show your work in detail.
(2) Present your work on a separate sheet (or separate sheets).
(3) Attach your work with this assignment sheet.
1. Give the
Math 131 - Fall, 2010 Homework 4 - Due Sept. 7 Name: _Solutions_
Mathematics Quote: Mathematics is the door and key to the sciences. - Roger Bacon (1214-1294)
Instructions for homework:
(1) Show your work in detail.
(2) Present your work on a separate she
Math 131 - Fall, 2010 Homework 5 - Due Sept. 10 Name: _Solutions_
Mathematics Quote: Mathematics is the science of what is clear by itself. - Carl Gustav Jacobi
(1804-1851)
Instructions for homework:
(1) Show your work in detail.
(2) Present your work on
Math 131 - Fall, 2010 Homework 6 - Due Sept. 14 Name: _Solutions_
Mathematics Quote: The infinite! No other question has ever moved so profoundly the spirit of man. David Hilbert (1862-1943)
Instructions for homework:
(1) Show your work in detail.
(2) Pre
Math 131 - Fall, 2010 Homework 8 - Due Sept. 24 Name: _Solutions_
Mathematics Quote: Mathematical discoveries, small or great are never born of spontaneous
generation They always presuppose a soil seeded with preliminary knowledge and well prepared by
lab
Math 131 - Fall, 2010 Homework 7 - Due Sept. 21 Name: _Solutions_
Mathematics Quote: In mathematics I can report no deficience, except it be that men do not
sufficiently understand the excellent use of the Pure Mathematics. - Roger Bacon (1214-1294)
Instr
Math 131 - Fall, 2010 Homework 13 - Due Oct 15 Name: _Solutions_
Mathematics Quote: The art of doing mathematics consists in finding that special case which
contains all the germs of generality. - David Hilbert (1862-1943)
Instructions for homework:
(1) S
Math 131 - Fall, 2010 Homework 12 - Due Oct 12 Name: _Solutions_
Mathematics Quote: In order to seek truth it is necessary once in the course of our life to doubt as
far as possible all things. - Rene Descartes (1596-1650)
Instructions for homework:
(1) S
Math 131 - Fall, 2010 Homework 11 - Due Oct 5 Name: _
Mathematics Quote: For a physicist mathematics is not just a tool by means of which phenomena
can be calculated, it is the main source of concepts and principles by means of which new theories can be
c
Math 131 - Fall, 2010 Homework 9 - Due Sept. 28 Name: _Solutions_
Mathematics Quote: "The invention of logarithms, by shortening the labors, double the life of the
astronomer." - Pierre-Simon Laplace (1749-1827)
Instructions for homework:
(1) Show your wo
Math 131 - Fall, 2010 Homework 10 - Due Oct 1 Name: _Solutions_
Mathematics Quote: "The invention of logarithms, by shortening the labors, double the life of the
astronomer." - Pierre-Simon Laplace (1749-1827)
Instructions for homework:
(1) Show your work
Math 131 Spring, 2006
Quiz 13(a)(b)
Name _Solutions_
Do not use a calculator for computing derivatives. Show your work in details.
(8pts) The graph of f x is given at the right.
y
(a) Find all critical numbers.
x 2, x 0, x 1
2.5
(b) Find where fx is incre
Math 131 Spring, 2006
Quiz 14(a)(b)
Name _Solutions_
Do not use a calculator for computing derivatives. Show your work in details.
1. (12pts) Evaluate the following indefinite integrals without using a calculator.
a.
3 3 x 2 e 3x sinx 2 dx 3x 1/2 x 1/3 2
Math 131 Spring, 2006
Quiz 7(a)(b)
Name _Solutions_
No calculator is allowed for this quiz. Use only the differentiation rules studied in sections (2.3) and
(2.4). Show your work in details.
1. (5pts) Let st t t 2 be a position function of a moving object
Math 131 Spring, 2006
Quiz 12(a)
Name _Solutions_
Do not use a calculator for computing derivatives. Show your work in details.
y
(6pts) The graph of f x is given below.
16
14
12
(a) Give the value of each critical number c of fx.
10
c 2, c 0, and c 1
8
6
Math 131 Spring, 2006
Quiz 8(b)
Name _
No calculator is allowed for this quiz. Use only the differentiation rules studied in sections (2.3)-(2.6).
Show your work in details.
1. (12pts) Compute f x without simplifying using differentiation rules studied in
Math 131 Spring, 2006
Quiz 10(a)(b)
Name _Solutions_
Do not use calculator for computing derivatives. Show your work in details.
dy
1. (10pts) Compute
where
dx
a. 3xy 3 4x 10y 2
i.
dy
dy
d 3xy 3 4x d 10y 2 ,
4 20y
3y 3 3x3y 2
dx
dx
dx
dx
ii.
dy
dy
4 3y
Math 131 Spring, 2006
Quiz 11(a)(b)
Name _Solutions_
Do not use calculator for computing derivatives. Show your work in details.
1. (6pts) A plane is moving horizontally x miles away from an airport at a constant altitude h 6 miles.
Let s be the distance
Math 131 Spring, 2006
Quiz 9(a)(b)
Name _Solutions_
No calculator is allowed for this quiz. Show your work in details.
(16pts) Compute f x (simplifying is not required).
1. fx 3 cotx 4 2 x cotx x 1 2 x 1/3
x
2/3
d cotx 4x 1 2 x
f x 1 cotx 4 2 x
x
3
dx
2/
Math 131 Spring, 2006
Quiz 5(a)(b)
Name _Solutions_
Show your work in details.
1. a. Find the equation of the tangent line to the curve y 2x 2 x 1 at the point where x 1.
f1 21 1 1 2
21 2h h 2 1 h 1 2
f1 h f1
21 h 2 1 h 1 2
m sec
h
h
h
4h 2h 2 h 3h 2h 2
Math 131 Spring, 2006
Quiz 3(a)(b)
1. (3pts) State the definition of continuity of a function f!x" at x ! a.
A function f is continuous at x ! a if
i. f!a" is defined;
ii. lim x"a f!x" exists; and
iii. lim x"a f!x" ! f!a".
Solutions
2. (4pts)
Version a. T
Math 131 Spring, 2006
Quiz 6(a)(b)
Name _Solutions_
No calculator is allowed for this quiz. Use only the differentiation rules studied in Section (2.3).
Show your work in details.
1. (9pts) Compute f x without simplifying .
1
a. fx x 2007
42 x 3 x 2007
Math 131 Spring, 2006
Quiz 2(a)(b)
Name _Solutions_
Find algebraically the following limits. Show your work in detail.
1. (2pts)
lim x0 sinx 2 sin0 sin 0
lim x0 cosx 2 cos0 cos 1
2. (3pts)
0
2
x 2x 1
x 2
0
lim x1
3 3
lim x1 x2 x 2 lim x1
1
x 1x 2
x 2
x