How do you use a Taylor series to expand: #f(x) = x^2 + 2x + 5# about x = 3? Calculus Power Series Constructing a Taylor Series 1 Answer Alan P. Jun 2, 2015 If #f(x) = x^2+2x+5# then #color(white)("XXXXX")##f'(x) = 2x+2# #color(white)("XXXXX")##f''(x)= 2# #color(white)("XXXXX")##f'''(x)" and beyond" = 0# The Taylor Series about #x=3# is #color(white)("XXXXX")##f(3)+(f'(3))/(1!)(x-3)+(f''(3))/(2!)(x-3)^2# #color(white)("XXXXX")##= 20 + 8(x-3) + (x-3)^2# Answer link Related questions How do you find the Taylor series of #f(x)=1/x# ? How do you find the Taylor series of #f(x)=cos(x)# ? How do you find the Taylor series of #f(x)=e^x# ? How do you find the Taylor series of #f(x)=ln(x)# ? How do you find the Taylor series of #f(x)=sin(x)# ? How do you use a Taylor series to find the derivative of a function? How do you use a Taylor series to prove Euler's formula? How do you use a Taylor series to solve differential equations? What is the Taylor series of #f(x)=arctan(x)#? What is the linear approximation of #g(x)=sqrt(1+x)^(1/5)# at a =0? See all questions in Constructing a Taylor Series Impact of this question 5794 views around the world You can reuse this answer Creative Commons License