By Daniel A. Murray
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Additional resources for A first course in infinitesimal calculus
The unit need not be a point or pebble as pictured here, but might be an arbitrarily chosen geometric magnitude, such as a line segment of a fixed length. Today we might choose a foot or a meter as our unit. If our measurements are of two-dimensional magnitudes, it would be natural to use a square, perhaps a square foot. In three dimensions a cube, per- 1. The Philosophy of Pythagoras 35 haps a cubic meter, might serve as the unit of reference. The essential thing is that, once a unit is established for discussion, the numbers of which we speak consist of multitudes of identical copies of the established unit.
Find an algebraic rule giving the area A in terms of L, and specifY the domain of this rule. 17. There is often more than one way to choose your variables. In problem 16, (a) Let xbe the amount of money spent on stone. How much is left to spend on wood, and how long, therefore, is the wooden fence? (b) Let x be the amount of money spent on stone. Find an algebraic rule giving A in terms of x, and specifY the domain of this rule. 18. A metal container, in the form of a rectangular solid, is to be constructed.
To answer the question raised in Example 1, we need to find the least number in the range of f, where f is the function whose rule of correspondence and whose domain are specified succinctly by writing 48 f(L)=7L+L, O
A first course in infinitesimal calculus by Daniel A. Murray