Math 142A — Midterm Page 4 of 11
2. (30 points A 1600 lb elevator is suspended by a 250 ft cable that weighs 10 lb / ft. How
much work is required to raise the elevator from the basement to the thlrd ﬂoor, a
height if 50 ft?
Math 142A - Midterm Page 3 of 11
. (a) (10 points) Sketch the region bounded by the curves f (:1: = 11:2 and g(:13) = x3.
0 Shade the region and clearly label each curve.
00 "' \“L ’1‘ ’
Math 142 - Quiz 2B
October 9, 2014
You have 30 minutes to complete this quiz. No calculators or collaboration is permitted.
Show your work! Answers without supporting work will not recieve full credit. (50 points)
Evaluate the following:
Lecture Notes for Section 8.1
A sequence is an infinite list of numbers written in a definite order:
2, 4, 8, 16, 32,
The numbers in the list are called the terms of the sequence. In the sequence above, the first
term is 2, the second term i
Limits at Infinity
To understand the ideas in chapter 8, we will need to have a better understanding of limits at
innity. We begin with a few examples.
EXAMPLE 1 Find lim 2 + 4
SOLUTION Note that both the numerator and deno
1. An ACME light bulb factory has secretly been dumping mercury for years, and it is now leaching
into a nearby stream. The stream carries water with a mercury concentration of 0.3 mg/ L into Lake
Wobegon, with an average discharg
A power series is a polynomial with infinitely many terms. Here is an example:
at) 2 1+x+m2+x3+m
Like a polynomial, a power series is a function of 1:. That is, we can substitute in different
values of m to get different resu