a.
To show: The function
a.
Explanation of Solution
Given information:
The function is.
Calculation:
The function is
Continuity at
Right hand limit of the function is as shown below.
Left hand limit of the function is as shown below.
Conclusion: Since, the right land limit , left hand limit and limit at a given point are equal. So, the function continuous at
b.
To show: The value of
b.
Explanation of Solution
Given information:
The function is.
Calculation:
The function is
Substitute the function in the left hand side,
Conclusion: Thus,
c.
c.
Explanation of Solution
Given information:
The function is.
Calculation:
The function is
Substitute the function in the left hand side,
Solve further.
Conclusion: Thus,
d.
To calculate: The left hand derivative and right hand derivative at
d.
Answer to Problem 48E
The right hand derivative and left hand derivative exist.
Explanation of Solution
Given information:
The function is.
Concept used:
The left hand derivative is
Calculation:
The function is
Right hand derivative is as shown below.
Left hand derivative is as shown below.
Conclusion: So, both right and left derivates exist.
e.
The function is differentiable at
e.
Answer to Problem 48E
The derivative exists.
Explanation of Solution
Given information:
The function is
Concept used:
The right hand derivative , left hand derivative should be equal.
Calculation:
The function is
Right hand derivative is as shown below.
Left hand derivative is as shown below.
Also
Conclusion: As the left hand derivative, right hand derivative and
Chapter 2 Solutions
CALCULUS-W/XL ACCESS
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