A Geometric Series In calculus, you will learn that certainfunctions can be approximated by polynomial functions. Wewill explore one such function now. (a) Using a graphing utility, create a table of values with1Y = f(x) =and Y, = g2(x) =1 + x + x² + x³1 - xfor -1 (b) Using a graphing utility, create a table of values withY = f(x) = -and1-x%3DY, = g,(x) = 1 + x + x² + x + x*for -1

Given: y1=11-x y2=g(x)=1+x+x2+x3

Answered: (a) Using a graphing utility, create a…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.4: The Slope-intercept Form Of A Linear Equation

Problem 16E

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A Geometric Series In calculus, you will learn that certain
functions can be approximated by polynomial functions. We
will explore one such function now.

(a) Using a graphing utility, create a table of values with
1
Y = f(x) =
and Y, = g2(x) =1 + x + x² + x³
1 - x
for -1 <x <1 with ATbl = 0.1.

(b) Using a graphing utility, create a table of values with
Y = f(x) = -
and
1-x
%3D
Y, = g,(x) = 1 + x + x² + x + x*
for -1 <x<1 with ATbl = 0.1.
(c) Using a graphing utility, create a table of values with
1
and
1- x
Y = f(x) =
Y, = g4(x) = 1 + x + x² + x* + x* + x
for -1 <x< 1 with ATbl = 0.1.
(d) What do you notice about the values of the function as
more terms are added to the polynomial? Are there some
values of x for which the approximations are better?

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