Approximation Theory

In class we showed that (2*x^3+x^2-2*x+11)/(x+2) = 2*x^2-3*x+4+3/(x+2) . I said that for large values of x, really |x|, one could approximate the left-hand-side with the quadratic polynomial on the right, ignoring the remainder. The graphs below illustrate this point. They were done with the program Maple V, available in the Math Department Computer Lab, Neckers 258.

> with(plots):

> plot([(2*x^3+x^2-2*x+11)/(x+2),2*x^2-3*x+4], x=-10..10,y=-100..100,color=[black,red],discont=true,thickness=2);

[Maple Plot]

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