(a)
The meaning of rejected quantity.
(a)
Answer to Problem 59E
The amount
Explanation of Solution
Given information:
The given statement:
“It is useful to consider quantities infinity small such that when their ratio is sought, they may not be consider zero, but which are rejected as often as they occur with quantities incomparably greater. Thus, if we have
Hence, if we are to differentiate
In the given statement the word “rejected” mean
“The small amount like a constant over infinity is so small it did not change anything and thus should be ignored to facilitate the problem."
Let
Hence, the amount
(b)
The status of the quantity
(b)
Answer to Problem 59E
The amount
Explanation of Solution
Given information:
The given statement:
“It is useful to consider quantities infinity small such that when their ratio is sought, they may not be consider zero, but which are rejected as often as they occur with quantities incomparably greater. Thus if we have
The given quantity is
Since,
Hence, the amount
(c)
To calculate: The value of the function.
(c)
Answer to Problem 59E
The expression results formula of product rule of the differentiation.
Explanation of Solution
Given information:
The given function is
Calculation:
The function is
Divide the above function each with respect to
Hence, the expression results formula of product rule of the differentiation.
(d)
Critics of Leibniz 's time objected to dividing the equation by
(d)
Answer to Problem 59E
The critics is “dividing by
Explanation of Solution
Given information:
The given function is
The quantity is
Since,
Hence, the critics is “dividing by
(e)
Critics of Leibniz 's time objected to dividing the equation by
(e)
Answer to Problem 59E
The Leibniz’s
Explanation of Solution
Given information:
The given functions are
Calculation:
The function are
Hence, the Leibniz’s division rule is
Chapter 3 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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