Calculus Volume 2

# Key Equations

Calculus Volume 2Key Equations
• Power series centered at $x=0x=0$
$∑n=0∞cnxn=c0+c1x+c2x2+⋯∑n=0∞cnxn=c0+c1x+c2x2+⋯$
• Power series centered at $x=ax=a$
$∑n=0∞cn(x−a)n=c0+c1(x−a)+c2(x−a)2+⋯∑n=0∞cn(x−a)n=c0+c1(x−a)+c2(x−a)2+⋯$
• Taylor series for the function $ff$ at the point $x=ax=a$
$∑n=0∞f(n)(a)n!(x−a)n=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n+⋯∑n=0∞f(n)(a)n!(x−a)n=f(a)+f′(a)(x−a)+f″(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n+⋯$