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Calculus II

More about e

e=(1+dx)1dx=limΔx0(1+Δx)1Δx=limN(1+1N)N
ex=limN(1+1N)Nx=limN(1+xNx)Nx
Nx
N
ex=limN(1+xN)N
ex=(1+xdx)1dx
n=0Cnxn=ex
n=0Cnnxn1=ex=n=0Cnxn
n=0Cnnxn1=n=1Cn+1(n+1)xn=c00x1+n=0Cn+1(n+1)xn=n=0Cnxn

More about e to the x

Cn+1(n+1)=Cn
Cn+1=Cnn+1
Cn=Cn1n
e0=1
C0=1
Cn=1n!
ex=n=0xnn!
e=n=01n!
n=0Cnxn=ex
n=0Cnnxn1=ex=n=0Cnxn
n=0Cnnxn1=n=1Cn+1(n+1)xn=c00x1+n=0Cn+1(n+1)xn=n=0Cnxn
Cn+1(n+1)=Cn
Cn+1=Cnn+1
Cn=Cn1n
e0=1
C0=1
Cn=1n!
ex=n=0xnn!

quoteint rule

(fg)=?
f(x)g(x)=h(x)
g(x)h(x)=f(x)
(g(x)h(x))=f(x)
g(x)h(x)+g(x)h(x)=f(x)
g(x)h(x)=f(x)g(x)h(x)
g(x)h(x)=f(x)g(x)f(x)g(x)
g(x)h(x)=f(x)f(x)g(x)g(x)
g(x)h(x)=f(x)g(x)g(x)f(x)g(x)g(x)
g(x)h(x)=f(x)g(x)f(x)g(x)g(x)
h(x)=f(x)g(x)f(x)g(x)g2(x)
(fg)=fgfgg2