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May
17
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
Continuity alone is not sufficient. Continuity plus two different solutions give an infinity of solutions. Think that $f$ Lipschitz (which is continuous) implies unique solution.
May
17
comment Show that $ \int_{-\infty}^{\infty} \frac{x^3}{(x^2+4)(x^2+1)}\, dx$ does not converge
If $a=b$ you integrate an odd function on $[-a,a]$ so you get $0$.
May
16
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
I do not get the question regarding the sufficiency. Can you please detail what you mean?
May
16
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
@S.Panja-1729: Wikipedia is only as right as the people contributing to it. So the question "is wikipedia wrong?" can well be answered "Yes" in plenty of situations. You can see in the comments to your questions that the equation you mention has infinitely many solutions.
May
16
answered Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers
May
16
revised Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
deleted 14 characters in body
May
16
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
Two solutions means exactly that. One may be trivial, there's no problem.
May
15
awarded  Notable Question
May
15
answered Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
May
15
reviewed Approve Twelve identical circles touching one another on the surface of a sphere
May
15
comment Accelerating approximations for arccos
Could you develop what you mean by the fact that you accelerated drastically the accuracy of $\arccos$? What was the rate of convergence before? What is your rate of convergence?
May
15
answered Twelve identical circles touching one another on the surface of a sphere
May
15
comment Are my results realistic or is there an error somewhere?
You know, you could include all the details of your problem in your question. If someone is willing to help, making him/her go through another question (without details), which links to a book, is not really appealing. Make your question self-contained, so that someone looking at it can understand what you ask without going through other sites/books.
May
15
answered $\sum \frac {1}{n^2 a_n}$ is divergent
May
14
comment Linear independence of $\sin(x)$, $\sin(2x)$, $\sin(3x)$ in Map($\mathbb{R},\mathbb{R}$)
Yes, but in your case, the family is not independent. Assume that there are $a,b,c$, such that the relation you wrote is true for all $x \in \Bbb{R}$. Now you choose three values for $x$, in order to find a system of equations satisfied by $a,b,c$. You can choose whatever values you like, since the relation is valid for all $x \in \Bbb{R}$. If the family is not dependent, you'll find, after a few tries, that $a=b=c=0$, and this means that you have independence.
May
14
answered How can I prove that $\frac{(3^n + 4^n)}{(4^n + 1)}, n \in \mathbb{N}$ is bounded?
May
14
answered Linear independence of $\sin(x)$, $\sin(2x)$, $\sin(3x)$ in Map($\mathbb{R},\mathbb{R}$)
May
14
answered Could someone explain how to solve these sets of equations please?
May
11
comment Limit of sequence - hard one
I have put a factor $1/n$ before the sum.
May
10
answered Limit of sequence - hard one