## Some definitions of exponential e, Mathematics

Assignment Help:

Some Definitions of e

1. 2.   e is the unique +ve number for which 3. 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 )

#### Example of addition, Example 1 Add 4x 4 + 3x 3 - ...

Example 1 Add 4x 4 + 3x 3 - x 2 + x + 6 and -7x 4 - 3x 3 + 8x 2 + 8x - 4 We write them one below the other as shown below.

#### Fractions, what is equizilent to 2/5

what is equizilent to 2/5

#### Explain histogramsin details, Explain Histogramsin details? Another way...

Explain Histogramsin details? Another way to display frequencies is by using a histogram. The following is an example of a histogram using the data from the previous example:

any tutorials?

#### Lognormal distribution, The Lognormal Distribution If ln(X) is a normal...

The Lognormal Distribution If ln(X) is a normally distributed random variable, then X is said to be a lognormal variable. If P1, P2, P3, ... are the prices of a scrip in per

#### Fractions, how do you multiply fractions

how do you multiply fractions

#### Relation between hieght, volume=(1/3)(pi)(radius of base)2(height) curved ...

volume=(1/3)(pi)(radius of base)2(height) curved surface area=(pi)(r)(l), r is radius of base and l is length of straight line connecting apex of cone with point on edge of base

#### Construct the finite automaton for state transition table, Construct the fi...

Construct the finite automaton for the state transition table given below. Ans: The finite automata is displayed below. The initial state is marked along with arrow sign a

#### Find the evaluation of angle, In parallelogram ABCD, ∠A = 5x + 2 and ∠C = 6...

In parallelogram ABCD, ∠A = 5x + 2 and ∠C = 6x - 4. Find the evaluation of ∠A. a. 32° b. 6° c. 84.7° d. 44° a. Opposite angles of a parallelogram are same in measu

#### Quantitative Technique in Marketing, a company''s advertising expenditures ...

a company''s advertising expenditures average \$5,000 per month. Current sales are \$29,000 and the saturation sales level is estimated at \$42,000. The sales-response constant is \$2,  