Calculus
Calculus
10th Edition
ISBN: 9781285057095
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Textbook Question
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Chapter 1.5, Problem 64E

Numerical and Graphical Reasoning A crossed belt connects a 20–centimeter pulley (10–cm radius) on an electric motor with a 40–centimeter pulley (20–cm radius) on a saw arbor (see figure). The electric motor runs at 1700 revolutions per minute.

Chapter 1.5, Problem 64E, Numerical and Graphical Reasoning A crossed belt connects a 20centimeter pulley (10cm radius) on an

(a) Determine the number of revolutions per minute of the saw.

(b) How does crossing the belt affect the saw in relation to the motor?

(c) Let L be the total length of the belt. Write L as a function of ϕ . where ϕ is measured in radians. What is the domain of the function? (Hint: Add the lengths of the straight sections of the belt and the length of the belt around each pulley.)

(d) Use a graphing utility to complete the table.

ϕ

0.3

0.6

0.9

1.2

1.5

L

(e) Use a graphing utility to graph the function over the appropriate domain.

(f) Find lim ϕ → ( π / 2 ) L.

(g) Use a geometric argument as the basis of a second method of finding the limit in part (f).

(h) Find lim ϕ → 0 L.

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Chapter 1 Solutions

Calculus

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