Useful life . An amusement company maintains records for each video game it installs in an arcade. Suppose that C ( t ) and R ( t ) represent the total accumulated costs and revenues (in thousands of dollars), respectively, t years after a particular game has been installed. If C ′ ( t ) = 2 and R ′ ( t ) = 9 e − 0.3 t then find the area between the graphs of C ′ and R ′ over the interval on the t axis from 0 to the useful life of the game and interpret the results.
Useful life . An amusement company maintains records for each video game it installs in an arcade. Suppose that C ( t ) and R ( t ) represent the total accumulated costs and revenues (in thousands of dollars), respectively, t years after a particular game has been installed. If C ′ ( t ) = 2 and R ′ ( t ) = 9 e − 0.3 t then find the area between the graphs of C ′ and R ′ over the interval on the t axis from 0 to the useful life of the game and interpret the results.
Solution Summary: The author shows the graph of the functions C(t) and R' over the interval on the t axis from 0.
Useful life. An amusement company maintains records for each video game it installs in an arcade. Suppose that C(t) and R(t) represent the total accumulated costs and revenues (in thousands of dollars), respectively, t years after a particular game has been installed. If
C
′
(
t
)
=
2
and
R
′
(
t
)
=
9
e
−
0.3
t
then find the area between the graphs of C′ and R′ over the interval on the t axis from 0 to the useful life of the game and interpret the results.
A function is defined on the interval (-π/2,π/2) by this multipart rule:
if -π/2 < x < 0
f(x) =
a
if x=0
31-tan x
+31-cot x
if 0 < x < π/2
Here, a and b are constants. Find a and b so that the function f(x) is continuous at x=0.
a=
b= 3
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 4x4) 5,
a = -1
lim f(x)
X--1
=
lim
x+4x
X--1
lim
X-1
4
x+4x
5
))"
5
))
by the power law
by the sum law
lim (x) + lim
X--1
4
4x
X-1
-(0,00+(
Find f(-1).
f(-1)=243
lim (x) +
-1 +4
35
4 ([
)
lim (x4)
5
x-1
Thus, by the definition of continuity, f is continuous at a = -1.
by the multiple constant law
by the direct substitution property
Chapter 6 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
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