By K. D. Stroyan
Calculus utilizing Mathematica
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Extra resources for Calculus Using Mathematica
T h e simplest linear function has t h e form y = m • x in (x, ^ - c o o r d i n a t e s . T h e parameter m is t h e slope of t h e line t h a t graphs t h e function. This linear function is increasing if m > 0, decreasing if m < 0 a n d horizontal (or constant) if m = 0. Calculus tells when a nonlinear function y = f[x] is increasing by computing an approximating linear function, the differential. ) It is easy t o tell if the linear function is increasing a n d t h e nonlinear function also increases where t h e approximation is valid...
Why? What are the restrictions on a and a? ma. 75, - 4 . 0 The animation uses the graphs to make a computer 'movie' of the graph sliding across the screen. The parts of the NoteBook left for you to work correspond to parts (2) and (3) above. 8. Background on Functional Identities You are familiar with the basic formulas for trig functions. General equations about an unknown function also play an important role in mathematics. 18, the basic operation of growth in 3 hours followed by growth for three more hours has to amount to growth in 6 hours.
A — area in sq. cm. s = length in cm. 1. Functions from Formulas 33 with domain s >0 A is a function of a single independent variable. The formula A = s2 makes perfectly good mathematical sense when s is negative but the geometrical meaning as length does not. Geometrically, the function A — A[s] has a domain restricted to s > 0. 1. Format for Homework. In homework problems involving applications we want you to (1) Explicitly list your variables with units and sketch a figure if appropriate. (2) Translate the information stated in the problem into formulas in your variables.