n(1+x)^(n-1) n is a constant. If f(x) = n(1+x)^(n-1) = [n].(1+x)^(n-1) then f'(x) = [n].(n-1)(1+x)^(n-2) (thanks to the chain rule) = (nČ-n).(1+x)^(n-2)....
You've differentiated the wrong function. Start with equation (2) n x(1+x)^(n-1) = Sum{C(n,k) k x^k} The LHS of this equation is n x(1+x)^(n-1) Differentiate,...
... I get it now. So the questions I'm posing are; 1)What is the notation for this method if this continues for higher degrees of the polynomials in k and n...
I Guess that everyone knows what are Closed Sets and Compact Sets . Give me a set which is finite , closed and not Compact . __________________________________...
I think it is not possible, a finite set is always compact (it doesnŽt matter if it is closed or not). A set is compact if for every open covering of it you...
Any set with finitely many elements is closed(since there are no limit points that are not in the set.) Likewise it is compact. This is true in every metric...
Easier proof----any topology on a set X is a subset of the power set P(X)= the set of all subsets of X. So if X has cardinality n < 00 then any open covering...
But the original post didn't say metric space......thinking whether it is true in non-separable spaces. Probably not, hunh. Say X is a set with topology :...
Whoops! When I incorrectly typed ... I should have typed "every sequence in the set has a subsequence which converges to a point in the set." And the sequence...
... This ... What's really important is that the compactness of a set S is a property depending on the topology of S and NOT on the topology the space S is...
... whether ... a ... You mean: every set which contains p0 is an open set and the empty set is open. OK ... closure ... this ... What did you try to prove ?...
... Hehe... It's so funny but it's true. Once I was playing a game of 500 with my friends (a card game), and I was keeping score. The score goes up only by...
I'm trying to differantiate y=x^(1/x) I got: dy/dx=(1/x)*x^(1/x-1)*(-1/x^2) using the power rule, chain rule and quotient rule, but that's apparently...
Logarithmic differentiation. y=x^(1/x) so log y = (1/x)logx by log rules of powers differentiate (1/y)(dy/dx)=(-x^-2)(log x) + (1/x)(1/x) by product rule =...
The power rule, like any other mathematical theorem, has hypotheses associated with it. It says that IF n is a CONSTANT then d/dx ( x^n ) = n x^(n-1) If you...
The derivative of e^x WOULD be x e^(x-1), but only if x were a constant (whioch is never is), e were a variable, and you were differentiating with respect to...
A Magic Matrix is a square number array such that the sums of the collums, rows, and diagonals all add to the same number. Prove or disprove there exist an...
I've never done this in text, so let me know how it werks out. You have to think of the first thing that comes to mind after the following questions! Scroll...
To differentiate y = x^(1/x) we use a process called 'logarithmic differnetiation' Ok i'll explain how it works. 1) Take natural log of both sides ln y =...
Hello, i need urgent help for obtaining the inverse of a matrix with 54 col and 54 rows and the values of the elements are from 10^-2 to 10^60 so when i used ...
The standard technique is to write the matrix on the left side of your paper, and the identity matrix on the right side. Then you go through some strategic...
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