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Mathematics
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Applied Calculus Study Set 1
Quiz 2: Functions, Limits, and the Derivative
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Question 201
Short Answer
Find
for the function
. Simplify your answer.
Question 202
Short Answer
Find function
such that
,
, and
.
Question 203
True/False
If f and g are functions, then
. Answer true or false.
Question 204
Short Answer
The number of IBM shares that Nancy owns is given by
. The price per share of the stock of IBM at time
is
dollars. What does the function
represent?
Question 205
Short Answer
Find the rules for the composite functions
and
.
,
Question 206
Short Answer
Find the functions
,
,
, and
.
,
Question 207
Short Answer
Let
,
, and
. Find the rule for the function
.
Question 208
Short Answer
Find function f such that
,
, and
.
Question 209
Short Answer
Let
,
. Find the rule for the function
.
Question 210
Short Answer
Let
,
. Find the rule for the function
.
Question 211
Multiple Choice
Let f be the function defined by
. Find
,
,
,
, and
.
Question 212
Short Answer
Let
,
and
. Find the rule for the function
.
Question 213
Short Answer
The 1980s saw a trend toward old-fashioned punitive deterrence as opposed to the more liberal penal policies and community-based corrections popular in the 1960s and early 1970s. As a result, prisons became more crowded, and the gap between the number of people in prison and the prison capacity widened. The number of prisoners (in thousands) in federal and state prisons is approximated by the function
where t is measured in years, with t = 0 corresponding to 1983. The number of inmates for which prisons were designed is given by
where C(t) is measured in thousands and t has the same meaning as before. Find an expression that shows the gap between the number of prisoners and the number of inmates for which the prisons were designed at any time t.
Question 214
Short Answer
TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $13,200 and a variable cost of $0.50/tape. Find a function C that gives the total cost incurred by TMI in the manufacture of x tapes/month.