(a.)
An equation for this tangent line.
(a.)
Answer to Problem 71E
It has been determined that an equation for the given tangent line is
Explanation of Solution
Given:
The line through the origin tangent to the graph of
Concept used:
The equation of a line passing through the origin and having slope
Calculation:
It is given that the line through the origin tangent to the graph of
Then, this tangent line passes through the origin and has slope
So,
Put
This is the required equation.
Conclusion:
It has been determined that an equation for the given tangent line is
(b.)
An argument based on the graphs of
(b.)
Answer to Problem 71E
It has been explained why
Explanation of Solution
Given:
The line through the origin tangent to the graph of
Concept used:
The equation of a line passing through the origin and having slope
Calculation:
As determined previously, the equation of the tangent is
The graphs of
It can be seen that the graphs of
It should also be noted that the graph of
This implies that
This is the required proof.
Conclusion:
It has been explained why
(c.)
To Show:
(c.)
Answer to Problem 71E
It has been shown that
Explanation of Solution
Given:
The line through the origin tangent to the graph of
Concept used:
The equation of a line passing through the origin and having slope
Calculation:
As shown previously,
Since
Now,
Multiplying both sides of the above inequality by
Simplifying using property of logarithm,
This is the required proof.
Conclusion:
It has been shown that
(d.)
To Show:
(d.)
Answer to Problem 71E
It has been shown that
Explanation of Solution
Given:
The line through the origin tangent to the graph of
Concept used:
The equation of a line passing through the origin and having slope
Calculation:
As shown previously,
Since the exponential function,
Now,
This implies that
Simplifying,
This is the required proof.
Conclusion:
It has been shown that
(e.)
Which is bigger;
(e.)
Answer to Problem 71E
It has been determined that that
Explanation of Solution
Given:
The line through the origin tangent to the graph of
Concept used:
The equation of a line passing through the origin and having slope
Calculation:
As shown previously,
Put
This implies that
Conclusion:
It has been determined that that
Chapter 3 Solutions
CALCULUS-W/XL ACCESS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning