91Ó°ÊÓ

Find the Taylor polynomials of degree \(n\) approximating the functions for \(x\) near \(0 .\) (Assume \(p\) is a constant.) $$\frac{1}{1-x}, \quad n=3,5,7$$

For Exercises \(1-9,\) find the first four nonzero terms of the Taylor series for the function about 0. $$(1+x)^{3 / 2}$$

Using known Taylor series, find the first four nonzero terms of the Taylor series about 0 for the function. $$e^{-x}$$

Using known Taylor series, find the first four nonzero terms of the Taylor series about 0 for the function. $$\sqrt{1-2 x}$$

For Exercises \(1-9,\) find the first four nonzero terms of the Taylor series for the function about 0. $$\sqrt[4]{x+1}$$

use Theorem 10.3 to find a bound for the error in approximating the quantity with a third-degree Taylor polynomial for the given function \(f(x)\) about \(x=0 .\) Compare the bound with the actual error. $$\sin (0.2), f(x)=\sin x$$

Find the Taylor polynomials of degree \(n\) approximating the functions for \(x\) near \(0 .\) (Assume \(p\) is a constant.) $$\frac{1}{1+x}, \quad n=4,6,8$$

Find the Taylor polynomials of degree \(n\) approximating the functions for \(x\) near \(0 .\) (Assume \(p\) is a constant.) $$\sqrt{1+x}, \quad n=2,3,4$$

For Exercises \(1-9,\) find the first four nonzero terms of the Taylor series for the function about 0. $$\sin (-x)$$

Using known Taylor series, find the first four nonzero terms of the Taylor series about 0 for the function. $$\cos \left(\theta^{2}\right)$$