Nitrogen prices. During 2001, nitrogen prices fell by 41%. Over the same year, nitrogen demand went up by 12%. (Source: Chemical week.) a. Assuming a linear change in demand, find the demand function, q ( x ) , by finding the equation of the line that passes through the points ( 1 , 1 ) and ( 0.59 , 1.13 ) . Here x is the price as a fraction of the January 2001 price, and q ( x ) is the demand as a fraction of the demand in January. b. As a percentage of the January 2001 price, what should the price of nitrogen be to maximize revenue?
Nitrogen prices. During 2001, nitrogen prices fell by 41%. Over the same year, nitrogen demand went up by 12%. (Source: Chemical week.) a. Assuming a linear change in demand, find the demand function, q ( x ) , by finding the equation of the line that passes through the points ( 1 , 1 ) and ( 0.59 , 1.13 ) . Here x is the price as a fraction of the January 2001 price, and q ( x ) is the demand as a fraction of the demand in January. b. As a percentage of the January 2001 price, what should the price of nitrogen be to maximize revenue?
Solution Summary: The author calculates the equation of the line that passes through the points (1,1) and
Nitrogen prices. During 2001, nitrogen prices fell by 41%. Over the same year, nitrogen demand went up by 12%. (Source: Chemical week.)
a. Assuming a linear change in demand, find the demand function,
q
(
x
)
, by finding the equation of the line that passes through the points
(
1
,
1
)
and
(
0.59
,
1.13
)
. Here x is the price as a fraction of the January 2001 price, and
q
(
x
)
is the demand as a fraction of the demand in January.
b. As a percentage of the January 2001 price, what should the price of nitrogen be to maximize revenue?
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
1. Compute
Lo
F⚫dr, where
and C is defined by
F(x, y) = (x² + y)i + (y − x)j
r(t) = (12t)i + (1 − 4t + 4t²)j
from the point (1, 1) to the origin.
Chapter 2 Solutions
Calculus and Its Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Bittinger, Ellenbogen & Surgent, The Calculus and Its Applications Series)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY