Maclaurin series express a function as a polynomial in powers of x using derivatives at 0, with general form f(x)=n=0∑∞n!f(n)(0)xn,
Maclaurin series allow us to approximate arbitrary functions as polynomials.
The Maclaurin series for a function f is given by
In summation form:
The Maclaurin series for ex is
The Maclaurin series for sinx is
The Maclaurin series for cosx is
The Maclaurin series for ln(x+1) is
The Maclaurin series for arctanx is
The binomial theorem can be extended to expansions with rational exponents (n∈Q):
Nice work completing Maclaurin Series Basics, here's a quick recap of what we covered:
Exercises checked off
Maclaurin series express a function as a polynomial in powers of x using derivatives at 0, with general form f(x)=n=0∑∞n!f(n)(0)xn,
Maclaurin series allow us to approximate arbitrary functions as polynomials.
The Maclaurin series for a function f is given by
In summation form:
The Maclaurin series for ex is
The Maclaurin series for sinx is
The Maclaurin series for cosx is
The Maclaurin series for ln(x+1) is
The Maclaurin series for arctanx is
The binomial theorem can be extended to expansions with rational exponents (n∈Q):
Nice work completing Maclaurin Series Basics, here's a quick recap of what we covered:
Exercises checked off