Some definitions of exponential e, Mathematics

Assignment Help:

Some Definitions of e

1.

104_defination of e.png

2.   e is the unique +ve number for which 342_defination of e2.png

3.

1684_defination of e3.png

The second one is the significant one for us since that limit is exactly the limit which we're working with above.  Thus, this definition leads to the following fact,

Fact 1

For the natural exponential function, f ( x ) = ex  we have

Hence, provided we are using the natural exponential function we obtain the following.

                                      f ( x )= ex       ⇒                f ′ ( x ) = ex

At this instance we're missing some knowledge that will let us to simply get the derivative for a general function.  We will be able to show that eventually for a general exponential function we have,

                            f ( x ) = a x   ⇒       f ′ ( x ) = a x ln ( a )


Related Discussions:- Some definitions of exponential e

How many balls must she select of the same colour, QUESTION (a) A bowl ...

QUESTION (a) A bowl contains ten red balls and ten blue balls. A woman selects balls at random without looking at them. i) How many balls must she select to be sure of havin

Multiplication and division , In multiplication and division we have 1) ...

In multiplication and division we have 1) Suggested ways of conveying the meaning of multiplication and division to children. These operations have to be taught as an activit

Explain multiplying-dividing negative fractions, Explain Multiplying/Dividi...

Explain Multiplying/Dividing Negative Fractions? There are 3 steps to multiplying or dividing fractions. 1. If any negative signs are present, place them next to the numerator

Use mathematical induction and prove equation, 1. Use mathematical inductio...

1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.

Probability exercise, 1. A psychologist developed a test designed to help p...

1. A psychologist developed a test designed to help predict whether production-line workers in a large industry will perform satisfactorily. A test was administered to all new empl

Critical point of exponential functions and trig functions, Critical point ...

Critical point of exponential functions and trig functions, Let's see some examples that don't just involve powers of x. Example:  find out all the critical points for the

Interval of validity, The interval of validity for an IVP along with initia...

The interval of validity for an IVP along with initial conditions: y(t 0 ) = y 0 or/and y (k) (t 0 ) = y k There is the largest possible interval on that the solution is va

Dynamic and kinematic viscosity , Tabulated values of the dynamic and kinem...

Tabulated values of the dynamic and kinematic viscosity of aqueous sodium chloride solutions have been researched in the academic literature (Kestin et al 1981). The data availab

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd