(a)
Tocalculate:The value of
(a)
Answer to Problem 42E
The derivation is
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Calculation:
Since,
Thus, the function will be
Find the derivatives of the function. Use the formula
Hence, for
(b)
To calculate:The value of
(b)
Answer to Problem 42E
The derivation is
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Calculation:
It is given that
Thus, the function will be
Find the derivatives of the function. Use the formula
Hence, for
(c)
To calculate:The value of
(c)
Answer to Problem 42E
The value of
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Calculation:
From 42a, for the value
Thus substitute the value 1 for
Hence, the value of
(d)
To calculate:The value of
(d)
Answer to Problem 42E
The value of
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Calculation:
From 42a, for the value
Thus substitute the value 1 for
Hence, the value of
(e)
Whether
(e)
Answer to Problem 42E
The limit
Explanation of Solution
Given information:
The given function:
Formula Used:
Condition for existence of two-sided limit:
Where
Calculation:
It is known that, for two sided limit
From 42c and 42d,
And,
Thus,
Hence, the limit
(f)
To calculate:The left hand derivative of
(f)
Answer to Problem 42E
The limit
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Calculation:
The given function be
Find the left hand derivative, use the formula
Write the above formula using the given function as:
(g)
To calculate:The right hand derivative of
(g)
Answer to Problem 42E
The right hand derivative does not exist.
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Calculation:
The given function be
For right sided limit,
Write the above formula using the given function as:
Thus, the limit of
Hence, right hand derivative does not exist.
(h)
Whether the derivative
(h)
Answer to Problem 42E
The right hand derivative does not exist.
Explanation of Solution
Given information:
The given function:
Formula Used:
Definition of the derivative:
Where
Calculation:
From 42f and 42g, the left hand derivative exist but the right hand derivative does not.
Hence, the derivative does not exist.
Chapter 3 Solutions
Calculus: Graphical, Numerical, Algebraic
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