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

Linear functions, Linear functions are of the form: y = a 0 ...

Linear functions are of the form: y = a 0 + a 1 x 1 + a 2 x 2 + ..... + a n x n where a 0 , a 1 , a 2 ..... a n are constants and x 1 , x 2 ..... x n a

Geometry, in right angle triangle BAC.

in right angle triangle BAC.

#title.simpal harmonic motion., #questionShow that the system oscillates in...

#questionShow that the system oscillates in simple harmonic motion demonstrated by; , for which the general solution where X = (x – x0)..

Dy/dx, how do you differentiate sinx/ex?

how do you differentiate sinx/ex?

Write prim's algorithm, Write Prim's Algorithm.   Ans: Prim's algorithm...

Write Prim's Algorithm.   Ans: Prim's algorithm to find out a minimum spanning tree from a weighted graph in step by step form is given below.  Let G = (V, E) be graph and S

Determine randomly generated bit string, Assume E is the event that a rando...

Assume E is the event that a randomly generated bit string of length 4 starts with a 1 and F is the event that this bit string consists of an even number of 1's. Are E and F indepe

Algebra, can I access algebra videos?

can I access algebra videos?

Emi, calculation of emi %

calculation of emi %

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