Concept explainers
(a)
Todetermine:The relationship between
(a)
Answer to Problem 39E
The required relationship between
Explanation of Solution
Given information:
The given function
Formula Used:
Condition for continuity:
Calculation:
The given function is
For
Now, find the continuity for
Consider
Find the left hand limit,
Now, find the right hand limit as
From the condition of continuity
Hence, the required relationship between
(b)
To calculate:The unique values for
(b)
Answer to Problem 39E
The required values are
Explanation of Solution
Given information:
The given function
Formula Used:
Definition of the derivative:
Where
Calculation:
From 39a
Let
The right hand derivative is found as
As
For the limit above to exist, the numerator must have
Now, divide
Since, the remainder is zero. Thus, take the limit of
For the differentiability left and right hand derivatives to be equal. Thus,
Now, calculate the value of
Hence, the required values are
Chapter 3 Solutions
Calculus: Graphical, Numerical, Algebraic
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