Taylor Series

Basic Series

100

f(x)=e^x

What is 

e^x=1+x+x^2/(2!)+x^3/(3!)

200

f(x)=sinx

What is 

sinx=x-x^3/(3!)+x^5/(5!)

300

f(x)=cosx

What is 

cosx=1-x^2/(2!)+x^4/(4!)

400

f(x)=1/(1-x)

What is 

1/(1-x)=1+x+x^2+x^3

500

f(x)=ln(1+x)

What is 

ln(1+x)=x-x^2/2+x^3/3

Operations

100

f(x)=e^(-x^2)

What is 

e^(-x^2)=1-x^2+x^4/(2!)-x^6/(3!)

200

f(x)=3sin(2x)

What is 

3sin(2x)=6x-(8x^3)/(2)+(3*32x^5)/(5!)

300

f(x)=cos(-x^2)

What is 

cos(-x^2)=1-x^4/(2!)+x^6/(4!)

400

f(x)=1/(1+3x)

What is

1/(1+3x)=1-3x+9x^2-27x^3

500

f(x)=ln(1+x^3)/2

What is 

ln(1+x^3)/2=x^3/2-x^6/4+x^9/6

Integration

100

int e^x dx

What is

x+x^2/2+x^3/(3*2!)+x^4/(4*3!)+c 

200

int sinx dx

What is 

x^2/2-x^4/(4*3!)+x^6/(6*5!)-x^8/(8*7!)+c

300

intcosxdx

What is

x-x^3/(3*2!)+x^5/(5*4!)-x^7/(7*6!)+c

400

int(1/(1-x))dx

What is 

x+x^2/2+x^3/3+x^4/4+c

500

intln(1+x)dx

What is

x^2/2-x^3/6+x^4/12-x^5/20+c

 

Differentiation

100

dy/dx(e^x)

What is 

1+x+x^2/2+x^3/6

200

dy/dx(sinx)

What is 

1-x^2/(2!)+x^4/(4!)-x^6/(6!)

300

dy/dx(cosx)

What is 

-x+x^3/(3!)-x^5/(5!)

400

dy/dx(1/(1-x))

What is 

1+2x+3x^2+4x^3

500

dy/dx(ln(1+x))

What is 

1-x+x^2-x^3