Using Calculus, it can be shown that the arctangent function can be approximated by the polynomial by the function shown below: f(x)= tan^-1(x) = (x)-(x^3/3)+(x^5/5)-(x^7/7)+(x^9/9)-(x^11/11) (where x is in radians) a. Evaluate f(1); f(10^9) and f(1.73205), what can ypu conclude from these values? b. Use a graphing utility to graph the arctangent function and its polynomial approximation on the same grid. How do the graphs compare. c. Study the pattern of the polynomial and guess the next term. Then repeat part (b). How does the approximation change when additional terms are added.

Using Calculus, it can be shown that the arctangent function can be approximated by the polynomial by the function shown below: f(x)= tan^-1(x) = (x)-(x^3/3)+(x^5/5)-(x^7/7)+(x^9/9)-(x^11/11) (where x is in radians) a. Evaluate f(1); f(10^9) and f(1.73205), what can ypu conclude from these values? b. Use a graphing utility to graph the arctangent function and its polynomial approximation on the same grid. How do the graphs compare. c. Study the pattern of the polynomial and guess the next term. Then repeat part (b). How does the approximation change when additional terms are added.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.5: Transformation Of Functions

Problem 5SE: How can you determine whether a function is odd or even from the formula of the function?

See similar textbooks