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

What percentage of the soda purchased was cola, 3/5 of the soda purchased a...

3/5 of the soda purchased at the football game was cola. What percentage of the soda purchased was cola? Change the fraction to a decimal through dividing the numerator through

#rounding off, I am the least two digit number which round off to 100?

I am the least two digit number which round off to 100?

Calculate the probability, Coal is carried from a rrrine in West Virginia t...

Coal is carried from a rrrine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 36 tons of coal in each ca

Determine the measurements of segments and angles, Determine the Measuremen...

Determine the Measurements of Segments and Angles Postulate 1.5 (The Distance Postulate) There is a unique positive number corresponding to every pair of points. Pos

Proof by Condratiction, "Prove by contradiction that no root of the equatio...

"Prove by contradiction that no root of the equation x^18 -2x^13 + x^5 -3x^3 + x - 2 = 0 is an integer divisible by 3" Any help would be very much appreciated!

Example of convergent or divergent - comparison test, Determine if the subs...

Determine if the subsequent series is convergent or divergent. Solution As the cosine term in the denominator doesn't get too large we can suppose that the series term

Dividing using compatible numbers, 4 friends have 235 marbles and want to s...

4 friends have 235 marbles and want to share.How many marbles should each friend receive?

Tutor, how can i apply as tutor

how can i apply as tutor

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