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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 )
While we first looked at mechanical vibrations we looked at a particular mass hanging on a spring with the possibility of both a damper or/and external force acting upon the mass.
10:30:45
1 ream uses 6% of a tree, Estimate the reams of paper used in one month in an office(may be your father, mother or neighbour), hence find the number of trees that need to be cut fo
Integration Integration is the reversal of differentiation An integral can either be indefinite while it has no numerical value or may definite while have specific numerical v
Union and Intersection - Set theory B ∩ C indicates the intersection of B and C. it is the set having all those elements that belong to both B and C If B = {5, 8, 11, 20, 2
1/cos(x-a)cos(x-b)
10 statements must be shown to be logically equivalent to the Statement the nxn matrix is invertible.
Properties of the Indefinite Integral 1. ∫ k f ( x ) dx = k ∫ f ( x ) dx where k refer for any number. Thus, we can factor multiplicative constants out of indefinite integral
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the sides of a right angle triangle are a,a+d,a+2d with a and d both positive.the ratio of a to d a)1:2 b)1:3 c)3:1 d)5:2 answer is (c) i.e. 3:1 Solution: Applying
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