#### To determine

**To find:**

(a) The value of number e

(b) Approximate value of e

(c) Natural exponential function

#### Answer

(a) The value of e = 1.

(b) Approximate value of e = 2.7

(c) fx=ex

#### Explanation

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.

**Conclusion:**

(a) The value of e = 1.

(b) Approximate value of e = 2.7

(c) fx=ex

(d)