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

Complex numbers, express the complex number z=5+i divide 2+3i in the form ...

express the complex number z=5+i divide 2+3i in the form a+ib

Exercise of concrete operational stage, Which of the following statements d...

Which of the following statements do you think are true about children? Indicate with 'T' for true and for false. Give reasons for your choice. a) Most primary school children a

Advantages and disadvantages of decision trees, Advantages of decision tree...

Advantages of decision trees 1. This clearly brings out implicit calculations and assumptions for all to see question and revise 2. This is simple to understand Disadvan

Find the curve on the surface - shortest arc lenght, (a) Find the curve on ...

(a) Find the curve on the surface z=x 3/2 joining the points(x,y,z)=(0,0,0) and (1,1,1) has the shortest arc lenght? (b) Use a computer to produce a plot showing the surface an

Positive integer, (a)   Specify that  the sum of  the degrees  of all verti...

(a)   Specify that  the sum of  the degrees  of all vertices of a graph  is double the number of edges  in  the graph.                            (b)  Let G be a non directed gra

Mathematics- in our lives , MATHEMATICS - IN OUR LIVES : What is the mo...

MATHEMATICS - IN OUR LIVES : What is the most obvious example of mathematics in your life? To many of us it is the maths that we studied in school. But is that all the mathemat

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