Recent content by jacksonjs20

Thank you very much. I would have been stuck for hours.

I'm trying to find a value K>o such that for real a,b,c,d (a^2+c^2)x^2+2(ab+cd)xy+(b^2+d^2)y^2 ≤ K(x^2+y^2). Any help on this would be greatly appreciated thanks.

I have come to the conclusion that g must be differentiable at x=0, and thus continuous, since the limit of the difference quotient from above and below exist and are equal. Is this correct? If so what is the most efficient method of proving that it is not differentiable at any other points...

let g:R->R be a real function defined by rule g(x) = x^2 if x\in\mathbb{Q} and g(x) = 0 if x\notin\mathbb{Q} is g continuous (*on R)? Many thanks in advance *thanks for pointing out mistake above.

Hi could someone please explain why (1-x^2)y'' = 2xy'-2y Many thanks in advance.

Hi, just a quick question. Let f be real function s.t. the limit of f as x approaches a equals L. Is f bounded? i.e. is it sufficient to assume a function is bounded if it has a limit. Thanks to all who may reply.

Thank you for your prompt reply. That is exactly the response i was looking for. Just to clarify The existence of an m > 0 is a necessary condition for a set to be bounded above. Though, provided it exists, an m < 0 which is an upper bound is sufficient to justify that a set is bounded above...

I have been consulting different sources of analysis notes. My confusion comes from these two definitions \begin{defn} Let S be a non-empty subset of $\mathbb{R}$. \begin{enumerate} \item $S$ is Bounded above $ \Longleftrightarrow\exists\,M > 0$ s.t. $\forall\, x\in S$, $x\leq M$...