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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 )
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Alternate Notation : Next we have to discuss some alternate notation for the derivative. The typical derivative notation is the "prime" notation. Though, there is another notation
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I don''t know how to do the next step like if I had 73 divided by 9 wouldn''t 7 go into nine 1 time then you have to do something else but that is the part I don''t understand
HOW TO ADD MIXED FRACTION
Determine how many square centimeters of paper are needed to make a label on a cylindrical can 45 cm tall with a circular base having diameter of 20 cm. Leave answer in terms of π.
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