Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Only #4
![for a,
(b) Solve e-(In 2)t = 1/10 for t, and then evalunte the number t o the nearest tenth.
2.) Consider two distinct functions f and g with the following properties:
(a) f(x) = x² for all z > 0.
(b) g is differentiable on (0, 0), g() 20 for all z2 0, and g(0) = 0.
(c) f'(x) < gʻ(x) for all æ 0.
Draw the graph of ƒ and a potential graph of g. What is the minimum possible value of g(4)? Explain
your answer.
* Let F, G, and H be differentiable on [1, 3], with F'(x) = G'(x) = H'(x) for all z in [1, 3]S^Assume that
the graph of F is as in the figure below, with F'(1) = 0 and F(3) = 2. If G(3) = 2, then sketch the
graph of G. If H(3) = 0, then sketch the graph of H, and find the value of H(1).
(4.)Consider the function f continuous on [-1,1], such that f(0) = 0, and
{
3x2 for – 1 < x < 0
2et – 2 for 0< x < 1
f'(x) =
Write down a formula for f on [-1,1], and then sketch the graph of f. (Hint: The rule of ƒ will have
2 parts, just as f' does. You will need to join the parts carefully, so f will be continuous on the whole
closed interval [-1, 1].
5. The world population satisfied approximately the following data:
2000: 6,080,000,000
1990: 5,321,000,000
In addition, it was predicted that the world population in 2010 would be 7,026,729,000. Assume that
the population has been and continues to grow exponentially.
1980: 4,458,000,000
(a) Using the data from 1980 and 1990, predict the population in 2010.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7ac3bc9-1f84-4079-9a69-898240237696%2F90192b25-5af7-44c7-ba2e-de6add14f004%2Fqch2qq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:for a,
(b) Solve e-(In 2)t = 1/10 for t, and then evalunte the number t o the nearest tenth.
2.) Consider two distinct functions f and g with the following properties:
(a) f(x) = x² for all z > 0.
(b) g is differentiable on (0, 0), g() 20 for all z2 0, and g(0) = 0.
(c) f'(x) < gʻ(x) for all æ 0.
Draw the graph of ƒ and a potential graph of g. What is the minimum possible value of g(4)? Explain
your answer.
* Let F, G, and H be differentiable on [1, 3], with F'(x) = G'(x) = H'(x) for all z in [1, 3]S^Assume that
the graph of F is as in the figure below, with F'(1) = 0 and F(3) = 2. If G(3) = 2, then sketch the
graph of G. If H(3) = 0, then sketch the graph of H, and find the value of H(1).
(4.)Consider the function f continuous on [-1,1], such that f(0) = 0, and
{
3x2 for – 1 < x < 0
2et – 2 for 0< x < 1
f'(x) =
Write down a formula for f on [-1,1], and then sketch the graph of f. (Hint: The rule of ƒ will have
2 parts, just as f' does. You will need to join the parts carefully, so f will be continuous on the whole
closed interval [-1, 1].
5. The world population satisfied approximately the following data:
2000: 6,080,000,000
1990: 5,321,000,000
In addition, it was predicted that the world population in 2010 would be 7,026,729,000. Assume that
the population has been and continues to grow exponentially.
1980: 4,458,000,000
(a) Using the data from 1980 and 1990, predict the population in 2010.
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