
Concept explainers
(a)
To find: The right-hand and left-hand limits of the given function at
(a)

Answer to Problem 29RE
The right-hand and left-hand limits both at
Explanation of Solution
Given information:
The given function is
Calculation:
The left-hand limit at
The right-hand limit at
The left-hand limit at
The right-hand limit at
The left-hand limit at
The right-hand limit at
Therefore, the right-hand and left-hand limits both at
(b)
To find:The function has limits if
(b)

Answer to Problem 29RE
The limit at
Explanation of Solution
Given information:
The given function is
Calculation:
From part (a), observed the limits of the function at
At
At
At
Therefore, the limit at
(c)
To find: The given function is continuous at points
(c)

Answer to Problem 29RE
The function is continuous at
Explanation of Solution
Given information:
The given function is
Calculation:
If the limit of a function is equal to the value of the function at that point, then the function is said to be continuous.
The limit at
So, the function is continuous at
The limit at
So, the function is discontinuous at
The limit does not exist at
Therefore, the function is continuous at
Chapter 2 Solutions
Calculus: Graphical, Numerical, Algebraic
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