FP2 Maclaurin and Taylor Series

$$e^x$$  

$$\sin x$$  

$$\cos x$$  

$$\frac{1}{1-x}$$  

$$e^x$$  

$$\sin x$$  

$$\cos x$$  

$$\frac{1}{1-x}$$  

$$e^x$$  

$$\sin x$$  

$$\cos x$$  

$$\frac{1}{1-x}$$  

$$\frac{40}{3}$$  

$$\frac{80}{3}$$  

80

240

480

x = 0

x = 1

x = e

x = c

$$\sum_{n=0}^{\infty}\frac{f^{\left(n\right)}\left(0\right)x^n}{n!}$$  

$$\sum_{n=0}^{\infty}\frac{f^{\left(n\right)}\left(c\right)\left(x-c\right)^n}{n!}$$  

$$\sum_{n=1}^{\infty}\frac{f^{\left(n\right)}\left(0\right)x^n}{n!}$$  

$$\sum_{n=1}^{\infty}\frac{f^{\left(n\right)}\left(c\right)\left(x-c\right)^n}{n!}$$  

$$1+x+x^2$$  

$$1+3x+6x^2$$  

$$1+3x+\frac{9}{2}x^2$$  

$$1+3x+9x^2$$  

$$x+x^3+x^5$$  

$$x-x^3+x^5$$  

$$2x+\frac{8}{3!}x^3+\frac{32}{5!}x^5$$  

$$2x-\frac{8}{3!}x^3+\frac{32}{5!}x^5$$