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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 )
Determine the tangent line to f ( x ) = 15 - 2x 2 at x = 1. Solution : We know from algebra that to determine the equation of a line we require either two points onto the li
project
100+5000
if two circles O and O''intersect in two points, A and B, the the line segment OO is what?
What is Faltings Theorem? Explain Faltings Theorem
Prove that A tree with n vertices has (n - 1) edges. Ans: From the definition of a tree a root comprise indegree zero and all other nodes comprise indegree one. There should
If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is
How to find total no. of unordered pairs of disjoint subsets of a finite set? Solution) Suppose A and B are two such disjoint subsets of the set S. Then every element can go into
the value of y for which x=-1.5
Whlie solving complex number 1pi in polar form.In book they have taken theta =-pi/4 why not 7pi/4 because the point lie in fourth quadrant and the theta is given by 2pi-angle(alpha
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