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Magazine Problem 6
Using known Taylor series, find the first four nonzero terms of the Taylor series about 0 for the function. $$t \sin (3 t)$$
Problem 7
For Exercises \(1-9,\) find the first four nonzero terms of the Taylor series for the function about 0. $$\sqrt[3]{1-y}$$
Problem 7
Find the Taylor polynomials of degree \(n\) approximating the functions for \(x\) near \(0 .\) (Assume \(p\) is a constant.) $$\arctan x, \quad n=3,4$$
Problem 7
Using known Taylor series, find the first four nonzero terms of the Taylor series about 0 for the function. $$\frac{1}{\sqrt{1-z^{2}}}$$
Problem 8
Find the Taylor polynomials of degree \(n\) approximating the functions for \(x\) near \(0 .\) (Assume \(p\) is a constant.) $$\tan x, \quad n=3,4$$
Problem 8
Using known Taylor series, find the first four nonzero terms of the Taylor series about 0 for the function. $$\frac{z}{e^{z^{2}}}$$
Problem 8
For Exercises \(1-9,\) find the first four nonzero terms of the Taylor series for the function about 0. $$\tan (t+\pi / 4)$$
Problem 8
Find the \(n^{\text {th }}\) Fourier polynomial for the given functions,
assuming them to be periodic with period 2 \(\pi\). Graph the first three
approximations with the original function.
$$f(x)=x^{2}, \quad-\pi
Problem 9
Find the Taylor polynomials of degree \(n\) approximating the functions for \(x\) near \(0 .\) (Assume \(p\) is a constant.) $$\frac{1}{\sqrt{1+x}}, \quad n=2,3,4$$
Problem 9
For Exercises \(1-9,\) find the first four nonzero terms of the Taylor series for the function about 0. $$\ln (5+2 x)$$
