Tuesday, October 11
−
Lecture 15 :
Related rates problems, velocity.
(Refers to
Section 4.2 in your text)
Students who have mastered the content of this lecture know about
:
Related rate problems.
Students who have practiced the techniques presented in this lecture will be able to
:
Recognize a
related rate problem, solve simple related rate problems.
Introduction – Related rate problems are ones where we calculate the rate of change of
one quantity in terms of the rate of change of another quantity. These questions are in the
form of word problems. To solve the problem we must recognize precisely what is given
and what is asked. Once we have recognized these…
…
the key to solving the related rates problem is to find an expression
which relates the quantities and then use the chain rule to differentiate the
expression with respect to time.
We provide the following examples as models to solve this type of problem.
15.1
Example
Air is being pumped into a spherical balloon so that its volume is
increasing at a rate of 100 cm
3
/min. How fast is the radius of the balloon increasing when
the diameter is 50 cm.
Solution:
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 Spring '11
 RobertAndre
 Calculus, 4 m, 3 m, 10 m, 10M

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