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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 )
give some examples
express the complex number z=5+i divide 2+3i in the form a+ib
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Advantages of decision trees 1. This clearly brings out implicit calculations and assumptions for all to see question and revise 2. This is simple to understand Disadvan
(a) Find the curve on the surface z=x 3/2 joining the points(x,y,z)=(0,0,0) and (1,1,1) has the shortest arc lenght? (b) Use a computer to produce a plot showing the surface an
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MATHEMATICS - IN OUR LIVES : What is the most obvious example of mathematics in your life? To many of us it is the maths that we studied in school. But is that all the mathemat
1/8 +2 3/4
what is a Benchmark Fraction
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