Chapter 4, Problem 151CR

(a)

To determine

To graph : the arctangent function and its polynomial approximation.

Explanation of Solution

Given information :

The polynomial approximation of arctangent function is as follows.

  $x-\frac{x^3}{3}+\frac{x^5}{5}-\frac{x^7}{7}$

Graph : The graph of arctangent function and its polynomial approximation is as follows.

  

Interpretation : the red curve represents arctangent and the blue curve represents the polynomial approximate $x-\frac{x^3}{3}+\frac{x^5}{5}-\frac{x^7}{7}$ .

(b)

To determine

To compare : the graph of arctangent function and its polynomial approximation.

Answer to Problem 151CR

The value of polynomial approximate and arctangent becomes approximately same as the value of $x$ tends to zero.

Explanation of Solution

Given information :

The polynomial approximation of arctangent function is as follows.

  $x-\frac{x^3}{3}+\frac{x^5}{5}-\frac{x^7}{7}$

Graph : The graph of arctangent function and its polynomial approximation is as follows.

  

Interpretation : the red curve represents arctangent and the blue curve represents the polynomial approximate $x-\frac{x^3}{3}+\frac{x^5}{5}-\frac{x^7}{7}$ . As the two curves coincides near origin , it can be concluded that value of polynomial approximate and arctangent becomes approximately same as the value of $x$ tends to zero.