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Nov
13
asked Number of subsets of a set having r elements
Jun
28
awarded  Commentator
Jun
28
comment Mathematics in the “ The Art of Computer Programming”
@AndréNicolas this is also one of the reasons.
Jun
28
comment Mathematics in the “ The Art of Computer Programming”
i am learning it for fun
Jun
28
revised How do I know which method of revolution to use for finding volume in Calculus?
added 182 characters in body
Jun
28
comment Mathematics in the “ The Art of Computer Programming”
So, I can study it just for the sake of maths and the analysis of algorithms and completely forget about the implementation of algorithms on computer?
Jun
28
answered How do I know which method of revolution to use for finding volume in Calculus?
Jun
28
comment Mathematics in the “ The Art of Computer Programming”
I am not trying to learn mathematics from this book. I have learnt the required topics from Concrete Mathematics. I am just studying the TAOCP to get anexperience of the real-life applications of the math that I've studied. By "right", I meant studying only the analysis of algorithms given in the book and not implementing them on the computer.
Jun
28
asked Mathematics in the “ The Art of Computer Programming”
Jun
24
asked Difference between proof and plausible argument.
Jun
24
answered How to prove that a series is convergent
Jun
24
comment Calculate the limit at x=0
This is my approach:- We have $\begin{align} f(x) & = \dfrac{\sqrt{a^2-ax+x^2}-\sqrt{a^2+ax+x^2}}{\sqrt{a-x} - \sqrt{a+x}}\end{align}$ $\begin{align} lim_{x\to0}f(x) & = lim_{h\to0}\dfrac{\sqrt{a^2-ah+h^2}-\sqrt{a^2+ah+h^2}}{\sqrt{a-h} - \sqrt{a+h}}\end{align}$ $\begin{align}& = \dfrac{\sqrt{a^2-0+0}-\sqrt{a^2+0+0}}{\sqrt{a-0} - \sqrt{a+0}}\end{align}$ $\begin{align}& = \dfrac{\sqrt{a^2}-\sqrt{a^2}}{\sqrt{a} - \sqrt{a}}\end{align}$ . Here I carried out the usual algebraic manipulations and got $2\sqrt{a}$
Jun
24
awarded  Editor
Jun
24
comment Calculate the limit at x=0
@Cocopuffs. How is it $\sqrt{a}$. This is my main problem. Please elaborate.
Jun
24
revised Calculate the limit at x=0
added a question.
Jun
24
asked Calculate the limit at x=0
Jun
24
awarded  Student
Jun
24
comment Calculate the limit of the given function at $x=0$
so what you suggested was just to avoid confusion due to the presence of a negatuve number, right? This means that if there was some other postive number in place of -1, then I could have used logarithm?
Jun
24
comment Calculate the limit of the given function at $x=0$
Thanks. Its just like $cosx$ when $x\to \infty$. It oscillates between 1 and -1. Here the Greatest integer function doesn't oscillate but still it can hold either of the two values - 1 or -1. right?
Jun
24
comment Calculate the limit of the given function at $x=0$
When $x$ approaches 0, $\frac1x$ approaches infinity. Then what can we say about $[\frac1x]$ ? You are claiming this to be 1 or -1. Why?