## Intermediate Value Theorem – Limits and Continuity

Posted: 12th February 2013 by seanmathmodelguy in Lectures

Intermediate Value Theorem To begin with, let’s start with the basic statement of the theorem. Theorem If $$f(x)$$ is continuous on a closed interval $$[a,b]$$ and $$N$$ is any number $$f(a) < N < f(b)$$ then there exists a value $$c \in (a,b)$$ such $$f(c) = N$$. The illustration corresponding to the theorem is to […]

## Continuity – Limits and Continuity

Posted: 12th February 2013 by seanmathmodelguy in Lectures

Continuity A function $$f(x)$$ is said to be continuous at a point $$a$$ in its domain if the following three properties hold. $$\displaystyle \lim_{x \to a} f(x)$$ exists. This takes three steps to show in itself. $$f(a)$$ has to exist, $$\displaystyle \lim_{x \to a} f(x) = f(a)$$. Continuity connects the behaviour of a function in […]

## Strategy to Calculate Limits – Limits and Continuity

Posted: 9th February 2013 by seanmathmodelguy in Lectures