Concept explainers
(a)
To find: The right hand and left hand limit of the given function at
(a)
Answer to Problem 30RE
The right hand limit of the function is
Explanation of Solution
Given information: The function is
Calculation:
The right hand limit of the given function at
The left hand limit of the given function at
Therefore, the right hand limit of the function is
(b)
To check: Whether the given function has limit as
(b)
Answer to Problem 30RE
No, the given function has no limit as
Explanation of Solution
Given information: The function is
Calculation:
From part (a) at
If at any point right hand limit is not equal to the left hand limit then the limit at that point does not exist. For the given function:
Therefore, the given function has no limit as
(c)
To find: The points of continuity of the given function.
(c)
Answer to Problem 30RE
The given function is only continuous at all point except the point
Explanation of Solution
Given information: The function is
Calculation:
From part (a) at
From part (b), the given function the limit as
The function is continuous at all points except the point
Therefore, the given function is only continuous at all point except the point
(d)
To find: The points of discontinuity of the given function.
(d)
Answer to Problem 30RE
The point of discontinuity of the given function is
Explanation of Solution
Given information: The function is
Calculation:
From part (c), it can be noticed that the given function is not continuous at point
Therefore, the point of discontinuity of the given function is
Chapter 2 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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Calculus: Early Transcendentals (2nd Edition)
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