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CALCULUS

INTEGRALS

v

THE NATURAL EXPONENTIAL FUNCTION

Dxe^u=e^uDxu

If u=g(x) and g is differentiable.

e^X=Y if and only if lnY=X

If X is any realnumber

The letter e denotes the poss. real mumber

lne=1

e~2.71828

to every real number X there corresponds exactly one positive real number Y such that lnY=X

Subtopic

lim as X appr. zero from the right, lnX= -infinity

X<0

lim as X appr. infinity, lnX=infinity

when X>0

Main topic