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Unformatted text preview: Name: TA: Math 10A. Midterm Exam 1 October 20, 2009 Sec. No: PID: Sec. Time: Turn off and put away your cell phone. You may use any type of calculator, but no other electronic devices during this exam. You may use one page of notes, but no books or other assistance during this exam. You may leave answers in symbolic form, for example 42 or ln(6). Read each question carefully, and answer each question completely. 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. # 1 2 3 4 Points 6 6 6 6 24 Score 1. (6 points) For parts (a)(e), use the following tables of values of the functions f and g. x 4 2 0 2 4 f (x) 4 1 2 5 8 x 0 1 2 3 4 g(x) 6 2 0 2 5 (a) Find g(f (4)) (b) Find f (0)g(0) (c) Find f 1 (g(1)) (d) Find g(g 1(2)) (e) One of the functions f and g is a linear function and the other is not. Find a formula for the linear function. 2. (6 points) You have 150 grams of a radioactive substance which decays exponentially. Each year the amount of the substance is reduced by 10%. (a) How much of the radioactive substance is left after 2 years? (b) Let Q(t) be the amount of the substance (in grams) after t years. Find a formula for Q(t) in terms of t. (c) What is the halflife of this substance? (i.e. How many years until only one half of the initial quantity remains?) 3. (6 points) Find a solution to the given equation. Please remember to show all of your work. (a) 12x1 = 3e4+x (b) 2 = 4 cos(2x  1) + 6 4. (6 points) Use the graphs of f and g to evaluate the given limit. If the limit does not exist, write "does not exist".
y
3 2 1 y y = f(x)
2 1 y = g(x) x
3 2 1 1 1 2 3 1 1 2 x (a) lim g(x)
x2 (b) lim f (x)
x1 (c) lim f (x)
x2 (d) lim [f (x) + g(x)]
x0 (e) lim f (x) x2 g(x) (f) lim g(x)
x ...
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This note was uploaded on 05/28/2010 for the course MATH 10A taught by Professor Arnold during the Spring '07 term at UCSD.
 Spring '07
 Arnold
 Math

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