Math 132
Fall 2007 Exam I
Notation:
D(f)(x) means: "the derivative of f evaluated at x." For example, if
3
2
f( x ) = x , then D( f )( x ) = 3 x and D( f )( 5 ) = 75.
N
f( s ) x for a function f on an interval [ a, b ] is said to be an
1. A Riemann sum
j
MATH 132 EXAMIII SOLUTIONS FALL 2008
PART I : ( 80 points)
1) Findthe sum ofthe series, 3 + 247'+ + % + , if it converges.
A) g B) % C)190 D) g % I) 55 J) diverges
DO
2) Find the limit ofthe sequence {(1,110)n } l , if it converges .
n:
A)0 B) 1 C)19C
Math 132 - Final Exam - Spring 2008
1
This exam contains 20 multiple choice questions. Each question is worth 5 points. 1. Find the arc length of y= x3 1 + 12 x
over the interval [1, 3]. (Hint: Use the identity 1 + (y )2 = (x2 /4 + x-2 )2 .) A) 8/13 B) 13
Math 132 - Exam I - Spring 2008
This exam contains 15 multiple choice questions and 2 hand graded questions. The multiple choice questions are worth 5 points each and the hand
graded questions are worth a total of 25 points. The latter questions will be
e
Math 132, Exam 2, March 71311
All questions carry equal marks. Choose the answer that is closest to the
solution (remember this means rounding the number, not just truncating it).
Trigonometric identities
sm2(:r:) = %[1cos(2$)]
~- %[1 + cos(2m)]
3111(3) c