# Introduction to Power Series - Page 2

Questions

- How do you find a power series representation for # f(z)=z^2 # and what is the radius of convergence?
- How do you find a power series representation for # x^2 / ( 1 - 2x )^2#?
- How do you find a power series representation for #ln(5-x) # and what is the radius of convergence?
- How do you find a power series representation for # f(x)= 9/(1-3x)^2 # and what is the radius of convergence?
- How do you find a power series representation for #e^x# and what is the radius of convergence?
- How do you find a power series representation for # f(x)=(x / (x^(2)-3x+2) )# and what is the radius of convergence?
- How do you find a power series representation for #ln(8-x)# and what is the radius of convergence?
- What is the Maclaurin Series for #tanax#?
- How do you find a power series representation for #f(x)=3/((1-5x)^2)# and what is the radius of convergence?
- How do you find a power series representation for #f(x)=1/(1+x)^3#?
- How do you find a power series representation for #1/(1-x)^2 # and what is the radius of convergence?
- How do you find a power series representation for #(1+x)/(1-x) # and what is the radius of convergence?
- How do you find a power series representation for # (1+x)/((1-x)^2)#?
- How do you find a power series representation for #e^(-x^2)# and what is the radius of convergence?
- How do you use a power series to approximate # int_0^1xtan^-1xdx #?
- How do you find the interval of convergence for a power series?
- How do you find a power series representation for #f(x)= x/(9+x^2)# and what is the radius of convergence?
- The exponential function #e^x# can be defined as a power series as: #e^x=sum_(n=0)^oo x^n/(n!)=1+x+x^2/(2!)+x^3/(3!)+...# Can you use this definition to evaluate #sum_(n=0)^(oo)((0.2)^n e^-0.2)/(n!)#?
- How do you find a power series representation for #ln(1-x)# and what is the radius of convergence?
- How do you find a power series representation for #ln(1-x^2) # and what is the radius of convergence?