91Ó°ÊÓ

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

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

Using known Taylor series, find the first four nonzero terms of the Taylor series about 0 for the function. $$\ln (1-2 y)$$

Which of the series are Fourier series? $$\frac{1}{2}-\frac{1}{3} \sin x+\frac{1}{4} \sin (2 x)-\frac{1}{5} \sin (3 x)+\cdots$$

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

Construct the first three Fourier approximations to the square wave function $$ f(x)=\left\\{\begin{array}{rr} -1 & -\pi \leq x<0 \\ 1 & 0 \leq x<\pi \end{array}\right. $$ Use a calculator or computer to draw the graph of each approximation.

Find the Taylor polynomials of degree \(n\) approximating the functions for \(x\) near \(0 .\) (Assume \(p\) is a constant.) $$\cos x, \quad n=2,4,6$$

Using known Taylor series, find the first four nonzero terms of the Taylor series about 0 for the function. $$\arcsin x$$

Using known Taylor series, find the first four nonzero terms of the Taylor series about 0 for the function. $$t \sin (3 t)$$

Find the Taylor polynomials of degree \(n\) approximating the functions for \(x\) near \(0 .\) (Assume \(p\) is a constant.) $$\ln (1+x), \quad n=5,7,9$$