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P112 Spring 2007
Homework #1
Due: Friday Jan 26, 2007 – At lecture
Reading: 1.11.6, 2.12.6
Not all concepts will be covered in class – you are responsible
for all material in the reading and in the homework problems.
Warmup Exercises:
(Answer only will be marked)
1. A bicycle travels 10 miles in 2 hours. What is its
average speed in miles per hour?
2. How long, in minutes, does it take to go to from
Ithaca to Syracuse (57 Miles away) if you travel at 65
miles per hour?
3. A bicycle, going up hill, travels 10 mile in 1 hour,
then, going down hill, it travels 10 miles in 30
minutes. What is the bicycle’s average speed in miles
per hour?
Mathematics Exercises:
4. Consider the function f(x)=
x
1+x
. What value does
f(x) take on as x becomes large?
5. Plot the function f(x)=
x
1+x
as a function of x, for
0<x<5.
6. What is the Taylor Expansion of f(x)=
x
1+x
about
x=0, to second order?
Estimation:
(Marked based solely on logic)
7. You are at Wegmans, and the parking lot is full.
Instead of driving around in circles you decide to sit
tight and “guard” a set of parking spots, hoping that
you will catch someone leaving. (a) Estimate how
many parking spots you can reasonably “guard”. (b)
Estimate how long the typical shopping trip lasts. (c)
Based on those estimates, how long do you think you
will have to wait before you get a parking spot?
Problems:
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 Spring '07
 LECLAIR,A
 mechanics, Work, The Land

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