MATH 205 Quiz: MATH 205 Louisville Quiz 1 150116
MATH 205–04 Quiz #1 Name:
Show all work. Arithmetic expressions do not need to be simplified in your final answer.
1. (7 points) This is the record of the first 5 minutes of a bicyclist’s trip:
Time elapsed (in minutes) 0 1 2 3 4 5
Distance traveled (in meters) 0 300 700 1050 1500 1800
(a) (2 points) What is the bicyclist’s average speed in the first two minutes of their journey?
(b) (2 points) What is the bicyclist’s average speed between the times t= 1 and t= 4?
(c) (3 points) The detailed records indicate that after 4.1 minutes (or 246 seconds), the
bicycle had gone 1539 meters. Based on this information, what would be a good estimate
for the instantaneous speed after 4 minutes?
2. (7 points) Calculate the following limits:
(a) lim
s→3
s2−6s+9
2s2−5s−3.
(b) lim
r→−2
r3−3r
r2+r−1.
3. (6 points) Below is the graph of a function f(x). For each of the six quantities listed, give its
value if it has a value, or specifically state that it does not exist.
.
.
1
.
1
lim
x→−3f(x) lim
x→1f(x)
lim
x→−1+f(x)f(1)
f(−1) lim
x→2+f(3)
4. (2 point bonus) If f(x) is an even function, and g(x) is an odd function, what do you know
for certain about the parity of f(f(x)), f(g(x)), g(f(x)), and g(g(x))? Show your work on the
back of this page.
Friday, January 16, 2015
Document Summary
Arithmetic expressions do not need to be simpli ed in your nal answer: (7 points) this is the record of the rst 5 minutes of a bicyclist"s trip: Based on this information, what would be a good estimate for the instantaneous speed after 4 minutes: (7 points) calculate the following limits: (a) lim s 3 s. 3 3r r2+r 1 : (6 points) below is the graph of a function f (x). For each of the six quantities listed, give its value if it has a value, or speci cally state that it does not exist. Show your work on the back of this page.
