Exercises 40–42 are related. Profit Equation Consider a coat factory with the cost and revenue equations given in Exercises 40 and 41. a. Find the equation giving the profit y resulting from making and selling x coats. b. Find and interpret the y -intercept of the graph of the profit equation. c. Find and interpret the x -intercept of the graph of the profit equation. d. Find and interpret the slope of the graph of the profit equation. e. How much profit will be made if 80 coats are sold? f. How many coats must be sold to have a profit of $6000? g. Draw the graph of the equation found in part ( a ).
Exercises 40–42 are related. Profit Equation Consider a coat factory with the cost and revenue equations given in Exercises 40 and 41. a. Find the equation giving the profit y resulting from making and selling x coats. b. Find and interpret the y -intercept of the graph of the profit equation. c. Find and interpret the x -intercept of the graph of the profit equation. d. Find and interpret the slope of the graph of the profit equation. e. How much profit will be made if 80 coats are sold? f. How many coats must be sold to have a profit of $6000? g. Draw the graph of the equation found in part ( a ).
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
4 Use Cramer's rule to solve for x and t in the Lorentz-Einstein equations of special relativity:x^(')=\gamma (x-vt)t^(')=\gamma (t-v(x)/(c^(2)))where \gamma ^(2)(1-(v^(2))/(c^(2)))=1.
Chapter 1 Solutions
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