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

Finding absolute extrema of f(x) on [a, Finding Absolute Extrema of f(x) on...

Finding Absolute Extrema of f(x) on [a,b] 0.   Confirm that the function is continuous on the interval [a,b]. 1.  Determine all critical points of f(x) which are in the inte

Relationship between the entries of a rotation matrix, 1. A 3d rotation mat...

1. A 3d rotation matrix has 9 (3 by 3) entries, and a 2d rotation matrix has 4 (2 by 2) entries. How many actual degrees of freedom are there in a 3d or 2d rotation? In other words

Inverse laplace transforms, Determining the Laplace transform of a function...

Determining the Laplace transform of a function is not terribly hard if we've found a table of transforms opposite us to use as we saw in the previous section. What we would want t

Compute the measure of the larger angle, Two angles are supplementary. The ...

Two angles are supplementary. The evaluate of one is 30 more than twice the measure of the other. Determine the measure of the larger angle. a. 130° b. 20° c. 50° d. 70

Vectors, apllication in business and economics

apllication in business and economics

Obtain the number of significant modes, On the Assessment page for the modu...

On the Assessment page for the module Moodle site you will find five frequency response functions for the frequency range 20 to 100 Hz in the EXCEL spreadsheet "FRF_Data". These a

The arithmetic mean, Arithmetic mean Arithmetic means is commonly know...

Arithmetic mean Arithmetic means is commonly known as average or mean it is acquired by first of all summing up the values provided and by dividing the total value by the tota

Linear programming , Use the simplex method to solve the following LP Probl...

Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0

Surds and logarithms, what are these all about and could i have some exampl...

what are these all about and could i have some examples of them please

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