2013/04/18
Calculus II Midterm
Total 105%
1~880%
Multiple choice5
1. Which of the following limits exist? (Multiple choice)
(A)
x2
(B)
( x , y )( 0, 0 ) x 2 y 2
(D)
2x2 y
(E)
( x , y )( 0, 0 ) x 4 y 2
lim
lim
xy cos y
( x , y )( 0, 0 ) 3x 2 y 2
lim
(C)
li

CHAPTER 27-28
PHYSICS II PART I
CHALLENGING PROBLEMS
26-78 A capacitor is constructed from two square, metallic plates of sides l and
separation d. Charges +Q and -Q are placed on the plates, and the power supply is
then removed. A material of dielectric

CHAPTER 26
PHYSICS II PART I
CHALLENGING PROBLEMS
26-65 Two square plates of sides l are placed parallel to each other with separation d.
Assume the condition of . The plates carry uniformly distributed static charges +0
and 0 . A block of metal has width

CHAPTER 29-30
PHYSICS II PART II
CHALLENGING PROBLEMS
29-61 The upper portion of the circuit is fixed. The horizontal wire at the bottom
has a mass of and a length of . The wire hangs in the gravitational field with an
acceleration of of the earth from id

CHAPTER 23
PHYSICS II PART I
CHALLENGING PROBLEMS
23-84 Identical thin rods of length 2a carry equal charges +Q uniformly
distributed along their lengths. The rods lie along the x-axis with their centers
separated by a distance b ( b > a ). Please calcula

Chapter 6
42. A childs toy consists of a small wedge that has an acute angle (Fig. P6.42). The
sloping side of the wedge is frictionless, and an object of mass m on it remains at
constant height if the wedge is spun at a certain constant speed. The wedge

Chapter 4
21. A firefighter, a distance d from a burning building, directs a stream of water from
a fire hose at angle i above the horizontal as shown in Figure P4.21. If the initial
speed of the stream is i, at what height h does the water strike the bui

Chapter 1
14. (a) Assume the equation x = At3 + Bt describes the motion of a particular object,
with x having the dimension of length and t having the dimension of time.
Determine the dimensions of the constants A and B. (b) Determine the dimensions
of th

Chapter 1
14. (a) Assume the equation x = At3 + Bt describes the motion of a particular object,
with x having the dimension of length and t having the dimension of time.
Determine the dimensions of the constants A and B. (b) Determine the dimensions
of th

CHAPTER 24&25
PHYSICS II PART I
CHALLENGING PROBLEMS
24-51 A sphere of radius R surrounds a particle with a charge Q, located at its
center. Find the electric flux through a circular cap of half-angle q.
kQ
E 2
r
E EdA
E
kQ
dA
2
r
dA rdq r sin q d
q
Q

Chapter 33
22. A capacitor C is connected to a power supply that operates at a frequency f and
produces an rms voltage V. What is the maximum charge that appears on either
capacitor plate?
P33.22
The maximum charge is given by
46. A resistor R, inductor L

Chapter 38
8. A screen is placed a distance L from a single slit of width a, which is illuminated
with light of wavelength . Assume L > a. If the distance between the minima
for m = m 1 and m = m2 in the diffraction pattern is y, what is the width of the

C.-M. Yang
Calculus (II) Midterm Exam
Date: 2015/04/23
:
(1)
(2) 110 2 3
(3)
1.
True-False (14%)
1
a.
Let =
cfw_ 1
2
. The Alternating Series Test can apply that
(-1)1 is convergent since lim = 0.
b.
There exists a power series
=0 ( ) whose interv

Calculus (II) Midterm Exam
Date: 2014/04/10
:
(1)
(2) 110 4
(3)
1.
Which of the following statements are true? (21%)
(A) If an > 0 n and limn n. an = L > 0, an is divergent.
(B) If an > 0 n and an converges, then (1)n an converges.
(C) If an > 0 limn0

Chapter 34.
16. Verify by substitution that the following equations are solutions to Equations
34.15 and 34.16, respectively:
E = Emax cos (kx t)
B = Bmax cos (kx t)
P34.16
We must show:
That is,
But this is true, because
The proof for the wave of the mag

Chapter 25
19. For the system of four capacitors shown in Figure P26.19, find (a) the equivalent
capacitance of the system, (b) the charge on each capacitor, and (c) the potential
difference across each capacitor.
Figure P26.19
P26.19
(a)
The equivalent c

Chapter 39
29. A moving rod is observed to have a length of, = 2.00 m and to be oriented at an
angle of = 30.0 with respect to the direction of motion as shown in Figure
P39.29. The rod has a speed of 0.995c. (a) What is the proper length of the rod?
(b)

Chapter 23
42. A uniformly charged rod of length L and total charge Q lies along the x axis as
shown in Figure P23.42. (a) Find the components of the electric field at the point
P on the y axis a distance d from the origin. (b) What are the approximate va

Chapter 4
21. A firefighter, a distance d from a burning building, directs a stream of water from
a fire hose at angle i above the horizontal as shown in Figure P4.21. If the initial
speed of the stream is i, at what height h does the water strike the bui

Chapter 16
29. Tension is maintained in a string as in Figure P16.29. The observed wave speed is
= 24.0 m/s when the suspended mass is m = 3.00 kg. (a) What is the mass per
unit length of the string? (b) What is the wave speed when the suspended mass is

Name:
National Chiao Tung University
Calculus II 0415 Exam ]4
Student Number:
Exam, Form: A
TA:
Date:
Part I: (8 points each) Compute the limit, if it exists, or show the limits does not exists. Show the steps of
your computation. Partial credit will be g

Name:
National Chiao Tung University
Calculus II 0415 Exam 2
Student Number:
Exam, Form: A
TA:
Date:
Section 1. True/False (2 points each)
Print T if the statement is true, otherwise print F
If
an is divergent, then
|an | is divergent.
1
is convergent.
ns

Name:
National Chiao Tung University
Calculus II 0415 Exam ]1
Student Number:
Exam, Form: A
TA:
Date:
Answer the problem in as thorough detail as possible. Be sure to include all your work. Partial
credit will be given even if the answer is not fully corr

Name:
National Chiao Tung University
Calculus 0415 Exam 4
Student Number:
TA:
Exam, Form: A
Date:
Optimization and Mean Value Theorem Problems: 10 points each
Answer the problem in as thorough detail as possible. Be sure to include all your work. Partial

Name:
National Chiao Tung University
Calculus 0415 Exam 2
Student Number:
Exam, Form: A
TA:
Date:
Answer the problem in as thorough detail as possible. Be sure to include all your work. Partial credit will be given
even if the answer is not fully correct.

Name:
National Chiao Tung University
Calculus 0415 Exam 3
Student Number:
Exam, Form: A
TA:
Date:
Answer the problem in as thorough detail as possible. Be sure to include all your work. Partial credit will be given
even if the answer is not fully correct.

Name:
National Chiao Tung University
Calculus 0415 Test 5
Student Number:
TA:
Exam, Form: A
Date:
Answer the indefinite integral problems as thorough detail as possible. Be sure to include all your work. Partial credit will
be given even if the answer is

Name:
National Chiao Tung University
Calculus 0415 Exam 1
Student Number:
Exam, Form: A
TA:
Date:
Write all your works in the Solution Booklet(s) and the form of your problem sheet on its cover! You may keep
and problem sheet after the test. No electronic

Chapter 21
22. A certain molecule has f degrees of freedom. Show that an ideal gas consisting of
such molecules has the following properties: (a) its total internal energy is fnRT/2,
(b) its molar specific heat at constant volume is fR/2, (c) its molar sp

Chapter 21
22. A certain molecule has f degrees of freedom. Show that an ideal gas consisting of
such molecules has the following properties: (a) its total internal energy is fnRT/2,
(b) its molar specific heat at constant volume is fR/2, (c) its molar sp

Chapter 19
24. A sample of a solid substance has a mass m and a density 0 at a temperature T0.
(a) Find the density of the substance if its temperature is increased by an amount
T in terms of the coefficient of volume expansion (b) What is the mass of the

Chapter 22
20. An ideal refrigerator or ideal heat pump is equivalent to a Carnot engine running
in reverse. That is, energy |Qc| is taken in from a cold reservoir and energy |Qh| is
rejected to a hot reservoir. (a) Show that the work that must be supplie

Chapter 14
15. Review. The tank in Figure P14.15 is filled with water of depth d = 2.00 m. At the
bottom of one sidewall is a rectangular hatch of height h = 1.00 m and width =
2.00 m that is hinged at the top of the hatch. (a) Determine the magnitude of