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By Smirnov V.I.

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Example text

Solve one equation for one variable in terms of the other. Substitute this expression into the other equations to determine the value of the first variable. Then substitute this value to determine the value of the other variable. CHAPTER 3: Systems of Equations and Partial Fractions 37 3. Elimination method. Apply the operations on equations leading to equivalent systems to eliminate one variable from one equation, solve the resulting equation for this variable, and substitute this value to determine the value of the other variable.

5 on the same coordinate system (Figure 4-10). Figure 4-9 Figure 4-10 Vertical Stretching and Compression The graph of y = af(x), for a > 1, is the same as the graph of y = f(x) stretched, with respect to the y-axis, by a factor of a. The graph of y = af(x), for 0 < a < 1, is the same as the graph of y = f(x) compressed, with respect to the y-axis, by a factor of 1/a. 17: For the basic function shown in Figure 4-8, graph y = f(x) and y = 2f(x) on the same coordinate system (Figure 4-11); y = f(x) and y = 1/3f(x) on the same coordinate system (Figure 4-12).

An improper rational expression can always be written, using the long division scheme, as a polynomial plus a proper rational expression. Any polynomial g can, theoretically, be written as the product of one A rational expression is any quotient of the form CHAPTER 3: Systems of Equations and Partial Fractions 33 or more linear and quadratic factors, where the quadratic factors have no real zeros (irreducible quadratic factors). It follows that any proper rational expression with denominator g can be written as a sum of one or more proper rational expressions, each having a denominator that is a power of a polynomial with degree less than or equal to 2.

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A course of higher mathematics, vol. 2 by Smirnov V.I.


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