Question Type 3: Maclaurin series using the formula Exercises

Find the Maclaurin series of $g(x)=\frac{\sin x}{x}$ up to and including the $x^6$ term.

Derive the Maclaurin series for $z(x)=\ln\frac{1+x}{1-x}$ up to $x^5$.

Use the Maclaurin series to find the first four nonzero terms of $f(x)=e^{x^2}$.

Find the Maclaurin series of $p(x)=\ln^2(1+x)$ up to and including the $x^3$ term.

Determine the Maclaurin series for $h(x)=e^x\cos x$ up to $x^5$.

Determine the Maclaurin series for $v(x)=\sin^3 x$ up to and including the $x^7$ term.

Find the Maclaurin polynomial of degree 4 for $w(x)=x e^x\cos x$.

Compute the Maclaurin series for $s(x)=\arctan x$ up to the $x^5$ term.

Find the Maclaurin series of $u(x)=(1+x)^{-2}$ up to $x^4$.