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Unformatted text preview: Name:
TA: PID:
Sec. No: Sec. Time: Math 10A.
Midterm Exam 1
January 28, 2011 Turn oﬀ and put away your cell phone.
You may use one page of notes, but no books or other assistance during this exam.
Read each question carefully, and answer each question completely.
√
You may leave answers in symbolic form, for example 42 or ln(6).
Show all of your work; no credit will be given for unsupported answers.
Write your solutions clearly and legibly; no credit will be given for illegible solutions.
If any question is not clear, ask for clariﬁcation. # Points Score 1 7 2 6 3 6 4 4 Σ 23 1. Given
f (x) = 5 − 2 cos (x)
3 , 1
g (x) = √ ,
x determine each of the following:
(a) (2 points) The domain of the composition f ◦ g . (b) (2 points) The amplitude and the period of the function f . (c) (1 point) The range of the function g . (d) (2 points) f (g −1 (2)) 2. Let f (x) = x2 x
.
− 25 (a) (2 points) Find the equation(s) of the vertical asymptote(s) of f . Please show
your work. (b) (2 points) Find the equation(s) of the horizontal asymptote(s) of f . Please show
your work. (c) (2 points) Find limx→2 f (x) or explain why the limit does not exist. Please show
your work. 3. Below is the graph of a function y = f (x). Use it to answer the following questions.
Assume the entire graph is shown.
3.5
3
2.5 f(x)
2
1.5
1
0.5
0 0.5 1 1.5 2 (a) (2 points) Evaluate the given limit. If the limit does not exist, write “does not
exist”. lim f (x) = x→0.5 lim f (x) = x→1+ (b) (1 point) Find f −1 (1). (c) (1 point) What is the range of f ? (d) (2 points) State all the values of a for which f (x) is not continuous at x = a. 4. (a) (2 points) Find the formula for the graph (0,2) 2 1.5 1 (2,1) 0.5 0 0
0 0.5 1 1.5 2 2.5 3 (b) (2 points) A biologist is researching a newlydiscovered species of bacteria. At
time t = 0 hours, he puts 100 bacteria into what he has determined to be a
favorable growth medium. Six hours later, he measures 450 bacteria. Assuming
continuous exponential growth, what is the growth constant ”k” for the bacteria? ...
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This note was uploaded on 09/07/2011 for the course MATH 10A taught by Professor Arnold during the Fall '07 term at UCSD.
 Fall '07
 Arnold
 Math, Calculus

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