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Unformatted text preview: Math 17A (Fall 2006)
Kouba Exam 1 Please PRINT your name here : __________________________________________________________
Your Exam ID Number ____________ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY
WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS
A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM
ANOTHER STUDENT’S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR
CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE
KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK
YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY
USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you
write down and how you write it are the most important means of your getting a good
score on this exam. Neatness and organization are also important. 5. Make sure that you have 6 pages, including the cover page. 6. You may NOT use L’Hopital’s Rule on this exam. 7. You may NOT use shortcuts for ﬁnding limits to infinity. 8. Using only a calculator to determine limits Will receive little or no credit.
9. You will be graded on proper use of limit notation. 10. You have until 8:50 am. sharp to ﬁnish the exam. 1.) (7 pts. each) Determine the following limits. . $2 — 4m + 3
a.) “1:113. 73—:— (HINT. Factor.)
b.) lim ————'$+2_1 (HINT: Use a conjugate or factor.)
:n—r—l :1: + 1
l _ l
c.) lim 2 “ (HINT: Add fractions ﬁrst.)
z—>2 2 — :1:
3 __
d.) $1320 %_—+:75—$ (HINT: Divide by a power of :12.)
2 —3
e.) lim + e :c—r—oo 6 — e‘a’ 2.) Consider the function f (:3) = 7  V611; — 2. a.) (3 pts.) Determine the domain of f. b.) (3 pts.) Determine the range of f. 3.) Start with a large piece of paper 1/64 of an inch thick (n = 0). Cut the paper in half
and place the pieces on top of each other to form a new stack (n = 1). Cut the new stack
in half and place the pieces on top of each other to form a new stack ( = 2). Let an be the thickness in inches of the stack after n cuts.
a.) (3 pts.) State the initial value (10 and give a recursion for an for n = 0, 1, 2, 3,   . b.) (7 pts.) Determine a1, a2, (13,, and a4 and determine an exponential growth formula
for an for n: 0,1,2,3,. c.) (5 pts. extra credit) How thick is the stack after the 28th cut ? Write your answer
in miles (1 mile = 5280 feet) ! 4.) a.) (10 pts.) Use limits and the concept of continuity to determine the value of constants A and B so that the following function is continuous for all values of (I). Start
Arc + B , if x < —1 { 3 , if —1 g a: S 2
m2 —— A , if :1: > 2 by drawing a “fake” graph. f(a:) = 3an+5
an—l 5.) (8 pts.) Determine all possible ﬁxed points for the following recursion : an+1 = 6.) (6 pts. each) Consider the function f(x) = 3 a: :13' a.) Show algebraically that f is oneto—one. b.) Determine y = f’1(2:), the inverse function for y : f(:1:). 7.) (6 pts. each) Find a formula for the nth term (starting with n=0) of each of the following sequences.
a.) 5, —7, 9, ~11, 13,  . b) 5,6,8,11,15,'20,26,...
(HINTzUsethefactthat1+2+3+4+...+n: ') 8.) (7 pts.) Use the Squeeze Principle to determine the limit of the following sequence : The following EXTRA CREDIT PROBLEM is worth 10 points. This problem is OP
TIONAL.
et — 5 1.) Consider the function N = W . Find all values of t for which N = 2. ...
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 Winter '10
 CRAIGBENHAM

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