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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 )
find the value of x for which [1 0] [0 x-8]
In polynomials you have seen expressions of the form x 2 + 3x - 4. Also we know that when an expression is equated to zero or some other expression, we cal
I have a maths assignment as- Use a newspaper to study and give a report on shares and dividends.
Suppose that we know the logarithms of all numbers which are expressed to base 'a' and we are required to find the logarithms of all these numbers to base 'b'. We
the function g is defined as g:x 7-4x find the number k such that kf(-8)=f- 3/2
/100*4500/12
Childrens errors are a natural and inevitable part of their process of learning. In the process of grasping new concepts, children apply their existing understanding, which may
Write following in terms of simpler logarithms. (a) log 3 (9 x 4 / √y) Solution log 3 (9 x 4 / √y) =log 3 9x 4 - log y (1/2) =log 3 9 + log 3 x 4
Example for Comparison Test for Improper Integrals Example: Find out if the following integral is convergent or divergent. ∫ ∞ 2 (cos 2 x) / x 2 (dx) Solution
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