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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 )
a deposit of 10,000 was made to an account the year you were born after 12 years the account is worth 16,600 what is the simple interest rate did the account earn?
Evaluate following. √16 and Solution To evaluate these first we will convert them to exponent form and then evaluate that since we already know how to
if you start a business and john creates 6 t shirts more than pedro and pedro four t shirts less than eva and between the three of then made 22 tshirts, how many t-shirts made each
Find the sum of first 40 positive integers divisible by 6 also find the sum of first 20 positive integers divisible by 5 or 6. Ans: No's which are divisible by 6 are
∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cosec2x - cot2x] + c = 1/2 log[tan x] + c Detailed derivation of ∫cosec x dx = ∫cosec x(cosec x - cot x)/(cosec x - cot x) dx = ∫(cosec 2 x
Consider the Van der Pol oscillator x′′- µ(1 - x 2 )x′ + x = 0 (a) Write this equation as a system of first order equations (b) Taking µ = 2, use MatLab's routine ode45 to
Table shows the productivity for the countries Pin and Pang. 1) If the working population of Pin and Pang are both 6 million, divided equally between the two industries in
Thus, just why do we care regarding direction fields? Two nice pieces of information are there which can be readily determined from the direction field for a differential equation.
find the unit rate. Round to the nearest hundredth in necessary 325 meters in 28 seconds
The first particular case of first order differential equations which we will seem is the linear first order differential equation. In this section, unlike many of the first order
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