By K. D. Stroyan
Calculus utilizing Mathematica
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Extra resources for Calculus Using Mathematica. Scientific Projects and Mathematical Background
We wanted ^ and approximated it in two steps, ^ x ^ . The chain rule says in general that % = %% when V is 'chained' together from two other functions. 7. Explain why the final expression AV ÄT*3FOC shows how the formula produces a large volume expansion from a small linear expansion, while at the same time, the length of the house is only changed a tiny amount using the formula Al ΔΤ=1°·° Now give a 'practical' application of your formula. 8. A worried homeowner hears of your computations and asks, 'How cold would it have to get to contract my house's volume by 1%?
We will see in Chapter 8 of the core text that the solution to the second equation isx = x$ecT. 0 x 10~ 6 . What do you observe? In particular, what is the largest difference between (1 + cT) and ecT over this range? 39 Chapter 5 Log and Exponential Functions in Science PROJECT 9 Drug Concentration and "Bi-Exponential" Functions Exponential functions arise in the study of the dynamics of drugs in the body. Here is a basic example. Suppose a drug is introduced into the bloodstream, say by an intravenous injection.
0307in This isn't very much, but how much would a house expand in volume? 35 Let's say the interior of the house is a rectangular solid 40 feet long, 30 feet wide and 8 feet high. 1. 84 cubic feet in volume, a thimble, a bucket or a EXERCISE bathtub? 2. A copper pipe runs down the 40 foot length of your house before warming. How much does it stick out the end of the house afterwards? How much force would be required to compress it back to the edge of the house? 3. How much does a gold palace the same size as your house expand its EXERCISE volume ?