I’ve received the following email from ICIAM and wanted to bring this to the wider mathematics community. Dear Colleagues, The January 2013 issue — Volume 1, No 1 — of the ICIAM Newsletter is now available. Please visit www.iciam.org/news to download a PDF copy of the Newsletter from the link that you will find there, … Read moreICIAM has a newsletter

Computing Limits I – Limits and Continuity

Computing  Limits I In order to compute a limit algebraically, one needs to know what is and more importantly what is not allowed when manipulating limits. For example consider computing$\lim_{x\to 1}\frac{x^2-1}{x-1}.$One cannot just substitute $$x=1$$ into this expression because doing so results in the indeterminate form $$0/0$$. By factoring the top of the … Read moreComputing Limits I – Limits and Continuity

Introduction to Limits – Limits and Continuity

Introduction to Limits The limit of a function is concerned with the behaviour of a function near a given point. What happens at the point is of no concern. To be more precise, if “the limit of the function $$f(x)$$ as $$x$$ approaches the point $$a$$” is the value $$L$$ then this is denoted as\[ … Read moreIntroduction to Limits – Limits and Continuity

Computing Limits II: The Squeeze Theorem – Limits and Continuity

The Squeeze Theorem Let’s start with a statement of the squeeze theorem. Theorem 1.1  Suppose $$g(x) \le f(x) \le h(x)$$ and this is true for all $$x$$ in a neighbourhood of $$x = a$$ (except perhaps at $$x = a$$). Further, suppose $$\displaystyle \lim_{x \to a} g(x) = \displaystyle \lim_{x \to a} h(x) = L$$. Then … Read moreComputing Limits II: The Squeeze Theorem – Limits and Continuity