Name:
Section:
Math 1571H.
Final Exam
December 14, 2006
There are a total of 235 points on this exam. It is a 3 hour exam with
caculators encouraged, but no notes or text. No other electronic devices
such as cell phones, headphones, etc. are permitted. To
MATH 1571H SAMPLE MIDTERM II PROBLEMS
October 29, 2013
INSTRUCTOR: Anar Akhmedov
The midterm exam will cover the Sections 3.1 - 3.6, 4.1 - 4.6
1. The sum of two positive numbers is 36. What is the smallest possible value of the sum of
their squares?
2. Fi
MATH 1571H SAMPLE MIDTERM III PROBLEMS
November 25, 2013
INSTRUCTOR: Anar Akhmedov
The midterm exam will cover the Sections 5.2 - 5.4, 6.2 - 6.7, 7.2 - 7.5.
1. Show that cos(x2 ) cos(x) for 0 x 1. Deduce that
/6
0
1
cos(x2 )dx .
2
2. Compute the integral
MATH 1571H SAMPLE FINAL PROBLEMS
December 8, 2013
INSTRUCTOR: Anar Akhmedov
The nal exam will cover the Sections 1.5, 1.6, 2.2 - 2.6, 3.1 - 3.6, 4.1 - 4.6, 5.2 - 5.4, 6.2 6.7, 7.2 - 7.5, 8.1 - 8.5, 9.1 - 9.5.
1. Find the limit, if it exists. If the limit
Page 2
x2 + 1
. Then f (1) is equal to
1. Let f (x) =
x+7
(A)
(B)
(C)
(D)
(E)
7
8
15
8
15
64
7
64
7
32
2. The tangent line to the curve y 2 = 3x2 + x + 2 at the point (-1,2) has equation
(A) y 2 = (3x2 + x + 2)(x + 1)
5
(B) y 2 = (x + 1)
4
5
(C) y 2 = (x
Math 1571H, Fall 2005
Solution to Quiz 8 (December 8)
Question 1. [5 points] Show that the work done in stretching a spring of natural length L
from a length a to a length b, where (L < a < b), is equal to the amount of stretch (b a) times
the tension in
Math 1571H, Fall 2005
Solution to Quiz 7 (November 17)
Please Answer The Following Three Questions, (Turn Over the Page.)
Question 1. [5 points] Find the volume of the solid of revolution generated when the area
bounded by the given curves is revolved aro
Math 1571H, Fall 2005
Solution to Quiz 6 (November 10)
This quiz is based on our celebrated Fundamental Theorem of Calculus (FTC):
Question 1. [3 points] Given f (x) is a continuous function such that
x
x
x2
(t2 et + 3)f (t)dt.
f (t)dt = e sin(x) +
0
(1)
Math 1571H, Fall 2005
Solution to Quiz 5 (October 27)
1) [3 points] Calculate the integral
(2x + 3)2
dx =
3
x
4x2 + 12x + 9
dx =
3
x
4x5/3 + 12x2/3 + 9x1/3 dx =
36x5/3 27x2/3
3x8/3
+
+
+ C.
2
5
2
2) [3 points] Compute the integrals by using the given subs
Math 1571H, Fall 2005
Solution to Quiz 4 (October 13)
1) [12 points] Give a graceful labeled sketch of the graph of
y=
1
x.
x1
You need to justify every step (i.e., Domain, asymptotes, xintercept, y intercept, symmetry, inection
points/concavity, local e
Math 1571H, Fall 2005
Solution to Quiz 3 (September 29)
1) [5 points] Find the distance between the lines
1
:
y3
z
x1
=
=
1
4
2
and
2
:
x+1
y+1
z2
=
=
.
1
2
0
Solution: Let 1 , 2 be the directions of 1 , and 2 respectively. 1 = i + 4j + 2k, and
uu
u
= i
Math 1571H, Fall 2005
Solution of Quiz 1 (September 15)
1) [6 points] Sketch the graph of y = x2 4. Find the equations of the two lines through the point (3, 1)
that are tangent to the curve y = x2 4. Use the fact that if f (x) = x2 4, then f (x0 ) = 2x0
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Name:
Section:
Math 1571H.
Practice Midterm Exam III
November 29, 2006
There are a total of 100 points on this exam, plus one 5-point extra credit
problem that you should only work if you complete the rest of the exam. To
get full credit for a problem you
Name:
Section:
Math 1571H.
Practice Midterm Exam II
November 1, 2006
There are a total of 100 points on this exam, plus one 5-point extra credit
problem that you should only work if you complete the rest of the exam. To
get full credit for a problem you m
Name:
Section:
Math 1571H.
Practice Midterm Exam I
There are a total of 100 points on this exam, plus a 5 point extra credit
problem that should not attempt unless you have nished the rest of the
exam. To get full credit for a problem you must show the de
MATH 1571H SAMPLE MIDTERM PROBLEMS
September 29, 2013
INSTRUCTOR: Anar Akhmedov
The midterm exam will cover the Sections 1.5, 1.6, 2.2 - 2.6.
1. Express the area of an equlateral triangle as a function of the length of a side.
2. (a) Represent function h(