a.
To Find: The derivatives of
a.
Answer to Problem 50E
Its limit is
Explanation of Solution
Given:
With the grapher in degree mode, graph
Compare the estimation with
Find the reason if any to believe the limit should be
Graph of
The value of
The value of
To Convert degrees to radians and vice versa:
Thus, the limit can be:
b.
To Estimate: The given function by setting the grapher in degree mode.
b.
Answer to Problem 50E
The value of the function
Explanation of Solution
Given:
With the grapher in degree mode, graph
Graph of the function
It can be seen from the graph, that the limit as
Thus,
c.
To Find: The formula that obtained for the derivative.
c.
Answer to Problem 50E
The formula that obtained for the derivative is
Explanation of Solution
Given:
Go back to the derivation of the formula for the derivative of
Considering the derivative:
Using the formula:
Apply limit to all the function:
Hence,
d.
To Derive: The formula for the derivative of
d.
Answer to Problem 50E
The formula for the derivative of
Explanation of Solution
Given:
Derive the formula for the derivative of
Given that,
Using the formula:
Here
Substituting the values into the formula:
Apply limit to all the function:
Hence,
e.
To Derive: The second and third degree-mode derivatives of
Explain the disadvantages of the degree-mode formulas become even more apparent
when taking derivatives of higher order.
e.
Answer to Problem 50E
The second order derivative of
The third order derivative of
The second order derivative of
The third order derivative of
Explanation of Solution
Given:
Derive the second and third degree-mode derivatives of
Given that the second and third order derivative of
The second order derivative of
The third order derivative of
Likewise, the second order derivative of
The third order derivative of
Chapter 2 Solutions
CALCULUS:GRAPHICAL,...,AP ED.-W/ACCESS
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