notes11 - Polynomial Approximations In comparison,...

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Unformatted text preview: Polynomial Approximations In comparison, polynomials are really simple. For example, without a calculator, you can compute every value of the polynomial p ( x ) = 1 + x + x 2 All you have to do is add and multiply. It may be hard if the numbers are big, but still, you could do it. One day you started to study more complicated functions, like sin( x ), cos( x ), e x and ln( x ). You probably felt confused, because now you dont know how to compute some values. For example e . 5 = e 1 / 2 = e 2 . 71828182 . . . And how on earth do you compute that? How does anyone? How does even a computer compute it? Math 9C Summer 2011 (UCR) Pro-Notes October 17, 2011 1 / 12 Its an amazing fact of nature that every function youve ever seen is actually a polynomial in disguise (kind of). And the world we know works by exploiting this fact. In 9A you began to study this. You did problems like: find the tangent line to the graph of the function f ( x ) at x = a . Why would anyone want to know that??? Math 9C Summer 2011 (UCR) Pro-Notes October 17, 2011 2 / 12 Lets find the tangent line to the function f ( x ) = e x at x = 0....
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notes11 - Polynomial Approximations In comparison,...

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