Concept explainers
(a)
Todetermine:Whether the function
(a)
Answer to Problem 48E
The function
Explanation of Solution
Given information:
The given function:
Formula Used:
Sandwich theorem:
If
Calculation:
Consider
Thus,
Use the sandwich theorem.
For any
Since,
Thus, by the sandwich theorem.
Hence, the function
(b)
To prove:
(b)
Answer to Problem 48E
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Proof:
The given function is
The given expression is
Substitute the value in the above expression.
Thus,
Hence proved.
(c)
The reason why
(c)
Answer to Problem 48E
The limit
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Calculation:
The value of
Thus, at
Hence,
(d)
Whether the function
(d)
Answer to Problem 48E
The value of
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Calculation:
The given function is
For the left hand derivative
Similarly for the right hand derivative
But from 48c,
Hence,
(e)
To calculate:The function
(e)
Answer to Problem 48E
The function
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Calculation:
The given function is
Find the derivative of
At
Hence, the function
Chapter 3 Solutions
Calculus: Graphical, Numerical, Algebraic
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