Math 30 - Calculus
Spring 2013
Tufts University Math Department
Exam 1
Feb 25, 2013
You may not use books, notes, or calculators during the exam. Solutions must be written in your exam book; cross
out any work you do not want graded. You are required to s
Math 30 - Calculus
Spring 2013
Tufts University Math Department
Exam 2
Apr 8, 2013
You may not use books, notes, or calculators during the exam. Solutions must be written in your exam book; cross
out any work you do not want graded. You are required to si
R EVIEW PROBLEMS FOR E XAM 2 - S PRING 2013
A FEW MORE PROBLEMS
Some of you expressed interest in a few more problems.
1. Find a function f ( x ) which has f ( x ) = 2 and f (1) = 2.
x
2. Compute the following indenite integrals.
(a)
2e x/4 dx
(b)
6
x
x
6
R EVIEW PROBLEMS FOR E XAM 2 - S PRING 2013
1. Differentiate the following functions. Simplify your answers as much as possible.
2
(a) y = xe x +1
(b) y =
1 + ln( x )
x
(c) f ( x ) = ln ( x + 1)( x2 + 1)
2. Write the equation of the tangent line to the cu
R EVIEW PROBLEMS FOR F INAL E XAM - M ATH 30 - S PRING 2013
1. Answer the following questions:
(a) What is the radian measure of 135 ?
(b) Find the angle s in radians for which cos(s) + 1 = 0 and 0 s 2 .
(c) Find cos(t) and sin(t) for the angle t in the d
Problems for Exam 1 - set A
1. For each of the following mathematical expressions, choose the correct simplication from the given list.
y5
(a) x y 1/3 =
x
(b)
s+t
st
2
=
x4/3 y11/2
(i)
(i)
s
t
+
t
s
,
,
(ii)
(ii)
x2/3 y11/2
s+
t
,
,
(iii)
s+t
(iii)
2. Fi
Review Problems for Exam 1 set B.
1. Factor the polynomial 2x3 4x2 4x as a product of linear factors.
( x 1)(3 x )
2. Find the domain of the function f ( x ) =
.
x 4
3. Simplify as much as possible the following expressions:
3
(a) 9 2
(b)
x 7 y2
3
x y 2
3