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Second Midterm Examination
Math 111, Winter 2004, Chris Phan
Tuesday, 2 March 2004
Name:
Please read, complete, and sign the following:
I, , completed the following examination in accordance the University’s policies on academic honesty. Specifically, I did not receive unauthorized assistance from another person and I did not use any unauthorized testing aids.
Signed:
- On the free-response questions, you mush show enough of your work so that I can follow your reasoning and method. Please answer clearly.
- Please put your answer in the space provided or put a box around your answer.
- You do not have to do the problems in order. Do the easy ones first.
- When you see the directions “Exact vales please!” do not give a decimal approximation for expressions like
2 or e.
- Good luck! Be sure to do all pages!
Problem Score Possible 1 12 2–4 9 5 10 6 4 7 4 8 6 10 (EC) 4 Total 45
Formulas for Midterm II
x = −b ±
b^2 − 4 ac 2 a √ (a − c)^2 + (b − d)^2 ( a + c 2
b + d 2
)
m = y 2 − y 1 x 2 − x 1 y = mx + b (y − y 0 ) = m(x − x 0 ) (x − c)^2 + (y − d)^2 = r^2 (f ◦ g)(x) = x and (g ◦ f )(x) = x f (x) = ax^2 + bx + c ( −b 2 a
, c − b^2 4 a
)
f (x) = h(x)q(x) + r(x) c^1 /n^ = n
c f (t) = P at f (t) = P ert M (t) = c(0. 5 t/h)
- True or false. Circle T if the statement is absolutely correct; otherwise, circle F. (2 points each)
(a) T F Every one-to-one function has an inverse. (b) T F The graph of f (x) = − 2 x^2 + 3 opens downward. (c) T F Every nth degree polynomial function has exactly n roots. (d) T F The equation x^5 = 1 has two real solutions. (e) T F If the graph of a function f has a vertical asymptote at x = 3, then 3 is not in the domain of f. (f) T F 10 x^ + 10y^ = 10xy^ for all real numbers x and y.
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Free-response. Please follow the instructions on the front page of the exam. Correct answers may include “undefined” or “no solution”.
- (10 points) Let
f (x) =
2 x x^3 − x
Find the vertical asymptote(s), hole(s), horizontal asymptote, x-intercept(s), and y-intercept(s) of f. Each of these may or may not exist. (Exact answers please.) Finally, create a complete graph of f from the information obtained above.
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- (4 points) I figured out why this room smells so bad. Someone placed some Stinkium, a smelly radioactive (but fortunately harmless!) element with a half-life of 20 years, inside the heating ducts for our classroom. I managed to scrape some of it out of there this morning, but there is still 100 g left that is caked on. We’ll just have to let it decay naturally. Write a function that gives the amount of Stinkium present after t years. How much Stinkium will remain in the duct 4 years from now? A decimal approximation is acceptable; however, show all work used to obtain such an approximation.
- (4 points) Solve for x: ex+
√ 3 = 1. (Exact answer please.)
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