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Unformatted text preview: Math 16A (Fall 2005)
Kouba
Exam 1 Please PRINT your name here : ___________________________________________________________
Your HW/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. 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. 2. No notes, books, or classmates may be used as resources for this exam. YOU MAY
USE A CALCULATOR ON THIS EXAM. 3. 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. 4. Make sure that you have 7 pages, including the cover page. You may NOT use L’Hopital’s Rule on this exam. You may NOT use shortcuts for ﬁnding limits to inﬁnity. Using only a calculator to determine limits" Will receive little credit. You will be graded on proper use of limit notation. $0.0ch? You have until 10:50 a.m. sharp to ﬁnish the exam.
10. The following trigonometry identities are at your disposal : a.) sin20=2sin0cos€
b.) c0820 2 2coszl9 — 1
= 1 — 2sin20
: c0526 — sin20 1.) (9 pts. each) Determine the following limits. , , x2 — 9
a.) {21—121 m (HINT. Factor.) — 2
b.) lim ﬂ
22—)4 x — 4 (HINT: Use a conjugate.) 1 1
__ + —
0.) lim I—H—ti (HINT: Add fractions ﬁrst.)
a: 2 2 —
d.) $11,120 ﬂ (HINT: Divide by the highest power of x.) 2.) Consider the function f(x) = 7 — «x — 3. a.) (4 pts.) Determine the domain of f. b.) (4 pts.) Determine the range of f. :I:+2
15—1 3.) (8 pts.) Let f(:z:) = . Find a function g(:c) so that f(g($)) = :c . 4.) a.) (5 pts.) Write the threestep deﬁnition for the following statement : Function
3/ : f(:c) is continuous at :15 = a. , b.) (5 pts.) Use the deﬁnition in part a.) to determine if the following function is
continuous at a: = 1.
x2+3x—1, ifx<l
f (:17) = 3 , if a: 2 1
«xv + 8 if x > 1 5.) (8 pts.) Solve the following trigonometry equation for 0 , 0 g 0 g 27r : 43in2 0 = 3 6.) (8 pts.) Use limits to ﬁnd the equati0n(s) for all vertical asymptote(s) for 2 _
y : Lil . YOU NEED NOT GRAPH THE FUNCTION.
(:1: + 1)(a: — 2)
p
7.) (8 pts.) Find all points of intersection, (any), for the functions y : $2+5I3 and
y = 2x2 — 2x + 2 . 8.) (8 pts.) The segment joining the points (1, 5) and (—2, 1) is the diameter of a circle.
Determine an equation for this circle. 9.) (6 pts.) Evaluate the following limit : lim (IE + 11:2 + 4) (HINT: Start with a $—) —00
conjugate.) ' Each of the following EXTRA CREDIT PROBLEMS is worth 10 points. These problems.
are OPTIONAL. 5
1.) Determine the domain for the following function : y : ——————
3 — m2 — 8x
_ , 2
35" 2.) Evaluate the following limit : $51132 Eggl—g—JZE—x ...
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 Spring '08
 Kouba
 Calculus

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