MTH 245 Calculus I
Test 2 (Chapter 2) Fall 2007
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1. (2 + 2 points) Find the average rate of change of the function over the given interval.
(a) f (x) = x2 3;
[1, 4]
Solution: Average rate of change of f (x) over the inte
MTH 245 Calculus I
Midterm I Fall 2007 Form A
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Select the correct answer.
1. Determine whether the function f (x) = x2 + x is even, odd, or neither.
(a) even
(b) odd
(c) neither even nor odd #
(d) not enough information to decode
MTH 245 Calculus I
Test 3C (Sections 3.8 to 3.10) Fall 2007
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1. (2+2 points) Find the following limits.
(a) limx tan1 x
Solution: limx tan1 x =
2
(b) limx1+ sin1 x
Solution: limx1+ sin1 x =
2
2. (3+3+3+3 points) Find t
MTH 245 Calculus I
Test 3C - (Sections 3.8 to 3.10) Fall 2007
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1. (2+2 points) Find the following limits.
(a) limx tan1 x
(b) limx1+ sin1 x
2. (3+3+3+3 points) Find the derivatives of the following functions.
(a) y = sin1 (x2 )
(b
MTH 245 Calculus I
Exam 4 (Chapter 4) Fall 2007
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1. (3 points) Find the absolute maximum and minimum values of the function f (x) = x2 8 ln x on the interval
[1, 3]. (ln 2 0.69 and ln 3 1.1)
8
Solution: f 0 (x) = 2x x .
MTH 245 Calculus I
Test 3B (Sections 3.5 to 3.7) Fall 2007
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1. (2+2+2+2 points) Find the derivatives of the following functions
(a) y = (3x 7)18
Solution:
d
(3x 7)
dx
= 18(3x 7)17 3
= 54(3x 7)17
y0
= 18(3x 7)17
(b) y =
MTH 245 Calculus I
Test 3A (Sections 3.1 to 3.4) Fall 2007
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1
1. (4 points) Use the denition of derivatives to nd the derivative of f (x) = x . Also nd f 0 (2).
Solution:
f (x + h) f (x)
h0
h
1
1
x
= lim x+h
h0
h
f 0 (x)
MTH 245 Calculus I
Chapter 4
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1. Find the absolute maximum and minimum values of each function on the given interval.
(a) f (x) = x3 3x,
2 x 2
0
Solution: f (x) = 3x2 3 = 3(x2 1) = 3(x 1)(x + 1). Thus,
f 0 (x) = 0
3(x 1
MTH 245 Calculus I
Test 1 (Chapter 1) Fall 2007
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1. (2 + 2 points) Find the domains of the following functions.
(a) f (x) = x2 + 5
Solution: Dom(f ) = (, ), i.e., all real numbers.
(b) g (x) = x 1
Solution: Dom(g ) = [1,