Exponential Function Form

Exponential function is a kind of equation. The exponential function can be represented by variables in the exponents. Exponential function is ex, this is in the form of f(x) = ax where a > 0 and not equal to 1. To work out the exponential equation, we have to use general log or natural log, logarithmic convention and also the exponential terms are separated.

Is this topic Limit of Exponential Function hard for you? Watch out for my coming posts.

Exponential series functional form:

The exponential series for ex is given by

ex = 1 + x + x2 / 2 ! + x3 / 3! +x4 / 4! + x5 / 5! + …..

The exponential series function for the trigonometric function sin x is given by

sin x = x – x3 / 3! + x5 / 5! - x7 / 7! + …..

The exponential series function for the trigonometric function cos x is given by

cos x = 1– x2 / 2! + x4 / 4! – x6 / 6! + …..

The exponential series function for complex function is eiθ

eiθ = cos θ + i sin θ.

Calculus exponential function form:

Calculus exponential function form is a common exponential function measured by integration and differentiation. General form of exponential function is

f(x) = ex or dx

Where x is a changeable variable and e is the stable term called the base of the function. Commonly the base term is indicated by the letter e called transcendental number.
Complex exponential function form:

The actual exponential function form can be represented in terms of the power series where,

∞
ex = ∑ (1/n!)xn
n=0

The complex exponential function is written as ez , and it can also be written as exp(z)

∞
exp (z) = ez = ∑ (1/n!)zn
n=0

If z = x + i y, where x and y are actual numbers, then ez = ex+iy

ez = ex . eiy

= ex (cosy + i siny)

= ex cosy + i ex siny.

Example for exponential function form:

For the function f(y) = 3y  + 5, find:

a) f(1)

b f(0)

c f(2)

Solution:

a)      f(1) = 3 (1) + 5

= 3 +5

f(1)= 8

I am planning to write more post on Subtracting Exponents and Definite Integrals Examples. Keep checking my blog.

b)      f(0) = 3 (0) + 5

= 1 + 5

f(0) = 6

c)      f(2)  = 3(2) + 5

= 9 +5

f(2)  =  14