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

Dora, dora and her family are driving to visit relatives for the holidays t...

dora and her family are driving to visit relatives for the holidays they travel 174 miles in 3 hours if they travel at a constant speed how many miles do they travel in one hourest

Trignometry, Sin3x ? Solution) THE FORMULA IS RIGHT ,SO sin3x=3sin...

Sin3x ? Solution) THE FORMULA IS RIGHT ,SO sin3x=3sinx-4sin 3 x

#mathematics induction, how many numbers must be selected from the set A={1...

how many numbers must be selected from the set A={1, 3, 5, 7, 9, 11, 13, 15}to guarantee that at least one pair of these numbers add up to16? Explain and justify your answer

Triangles, if A be the area of a right triangle and b be one of the sides c...

if A be the area of a right triangle and b be one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2Ab/rootb^4+4A^2

Example of addition of signed numbers, Example of addition of Signed Number...

Example of addition of Signed Numbers: Example: (-2) + 3 + 4 = 0 - 2 + 3 + 4 Solution: Thus: (-2) + 3 + 4 = 5  Example: 10 + (-5) + 8 + (-7)

Substitution rule, Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (...

Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (u ) du,     where, u = g ( x ) we can't do the following integrals through general rule. This looks considerably

Geometry, all basic knowledge related to geometry

all basic knowledge related to geometry

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