(a)
To check: The statement is true or false.
(a)
Answer to Problem 44E
The statement is true.
Explanation of Solution
Given information:
Calculation:
The above statement is understood to be the limit of
Therefore the statement is true.
(b)
To check: The statement is true or false.
(b)
Answer to Problem 44E
The statement is false.
Explanation of Solution
Given information:
Calculation:
The given statement might be interpreted as meaning that there is no
Follow the function's graph from the left and get close to
Follow the function's graph from the right and get close to
The left-hand and right-hand limits both exist and are equal at 1, therefore the limit does exist and the assertion is false.
(c)
To check: The statement is true or false.
(c)
Answer to Problem 44E
The statement is false.
Explanation of Solution
Given information:
Calculation:
As x gets closer to 2, the limit of
Follow the function's graph from the left and get close to
Follow the function's graph from the right and get close to
The claim is false because the left-hand and right-hand limits are 1 and not 2, respectively.
(d)
To check: The statement is true or false.
(d)
Answer to Problem 44E
The statement is true.
Explanation of Solution
Given information:
Calculation:
According to the given assertion, the limit of
Therefore the required given statement is true.
(e)
To check: The statement is true or false.
(e)
Answer to Problem 44E
The statement is true.
Explanation of Solution
Given information:
Calculation:
If trace the graph as move toward
Therefore the required given statement is true.
(f)
To check: The statement is true or false.
(f)
Answer to Problem 44E
The statement is true.
Explanation of Solution
Given information:
Calculation:
If the left and right have different boundaries, then there won't be a limit. In fact, discovered:
The limit as defined by
Therefore the required given statement is true.
(g)
To check: The statement is true or false.
(g)
Answer to Problem 44E
The statement is true.
Explanation of Solution
Given information:
Calculation:
If the limit on both sides is the same as x gets closer to zero. The graph reaches the point
Now if follow the graph's path from the right, see that it tends to head in the same direction.
The statement is true because the boundaries are equal.
(h)
To check: The statement is true or false.
(h)
Answer to Problem 44E
The statement is true.
Explanation of Solution
Given information:
Calculation:
There is a limit for every c in the open interval
(i)
To check: The statement is true or false.
(i)
Answer to Problem 44E
The statement is true.
Explanation of Solution
Given information:
Calculation:
This is accurate since the interval notation
Therefore the required given statement is true.
Chapter 1 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning