T 69. Which is bigger, 7 or e™? Calculators have taken some of the mystery out of this once-challenging question. (Go ahead and check; you will see that it is a surprisingly close call.) You can answer the question without a calculator, though. a. Find an equation for the line through the origin tangent to the graph of y = In x. [-3, 6] by [–3, 3] b. Give an argument based on the graphs of y = ln x and the tangent line to explain why In x < x/e for all positive x + e. c. Show that In (xª) < x for all positive x e. d. Conclude that xº < e* for all positive x # e. e. So which is bigger, º or e™?
T 69. Which is bigger, 7 or e™? Calculators have taken some of the mystery out of this once-challenging question. (Go ahead and check; you will see that it is a surprisingly close call.) You can answer the question without a calculator, though. a. Find an equation for the line through the origin tangent to the graph of y = In x. [-3, 6] by [–3, 3] b. Give an argument based on the graphs of y = ln x and the tangent line to explain why In x < x/e for all positive x + e. c. Show that In (xª) < x for all positive x e. d. Conclude that xº < e* for all positive x # e. e. So which is bigger, º or e™?
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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![T 69. Which is bigger, 7 or e™? Calculators have taken some of
the mystery out of this once-challenging question. (Go ahead and
check; you will see that it is a surprisingly close call.) You can
answer the question without a calculator, though.
a. Find an equation for the line through the origin tangent to the
graph of y = In x.
[-3, 6] by [–3, 3]
b. Give an argument based on the graphs of y = ln x and the
tangent line to explain why In x < x/e for all positive x + e.
c. Show that In (xª) < x for all positive x
e.
d. Conclude that xº < e* for all positive x # e.
e. So which is bigger, º or e™?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F690b93c1-a36f-4ba6-8aab-a0d4b7e86b05%2F2460c574-f63a-4683-b66f-a2ce2eb2c7cd%2Flfit64x.png&w=3840&q=75)
Transcribed Image Text:T 69. Which is bigger, 7 or e™? Calculators have taken some of
the mystery out of this once-challenging question. (Go ahead and
check; you will see that it is a surprisingly close call.) You can
answer the question without a calculator, though.
a. Find an equation for the line through the origin tangent to the
graph of y = In x.
[-3, 6] by [–3, 3]
b. Give an argument based on the graphs of y = ln x and the
tangent line to explain why In x < x/e for all positive x + e.
c. Show that In (xª) < x for all positive x
e.
d. Conclude that xº < e* for all positive x # e.
e. So which is bigger, º or e™?
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