Question Type 1: Maclaurin series with substitution Exercises

Find the Maclaurin expansion of $f(x)=\sqrt{1+2x}$ up to and including the $x^3$ term.

Obtain the Maclaurin series for $f(x)=\arctan(2x)$ up to and including the $x^5$ term.

Determine the Maclaurin series for $f(x)=e^{5x}$ up to and including the $x^4$ term.

Determine the Maclaurin series of $f(x)=(1+2x)^{-\frac{1}{2}}$ up to and including the $x^3$ term.

Find the Maclaurin series for $f(x)=\ln\bigl(1+2x^3\bigr)$ up to and including the $x^9$ term.

Find the Maclaurin expansion of $f(x)=\ln\bigl(1-x^2\bigr)$ up to and including the $x^6$ term.

Find the Maclaurin series of $f(x)=\frac{1}{1-x^2}$ up to and including the $x^6$ term.

Find the Maclaurin series expansion of $f(x)=\arctan(3x^2)$ up to and including the $x^6$ term.

Find the Maclaurin series for $f(x)=\dfrac{e^x-1}{x}$ up to and including the $x^3$ term.

Determine the Maclaurin series for $f(x)=\dfrac{1}{\sqrt{1+3x}}$ up to and including the $x^3$ term.

Find the Maclaurin series expansion of $f(x)=\sin(4x^2)$ up to and including the $x^6$ term.

Obtain the Maclaurin series of $f(x)=\ln\left(\frac{1+x}{1-x}\right)$ up to and including the $x^5$ term.