(a) The value of number e
(b) Approximate value of e
(c) Natural exponential function
(a) The value of e = 1.
(b) Approximate value of e = 2.7
a) The number e is defined as limh→∞(eh-1)/h=1.
Geometrically, this means that of all the possible exponential functions y=bx, the function fx=ex is the one whose tangent line at (0,1) has a slope f'0=1 (because f'x=ex).
b) The approximate value for the number e is 2.71828182845904523….
c) The function fx=ex is the known as the natural exponential function.