Sketch the functions $g(x), h(x), $ and $ f( x)$ such that
the following conditions hold.
\begin{align*}
a) &\lim_{x \to 5}{g(x)} = 10 \text{however} g(5)
\text{is not defined.}\hskip2truein\\
b) &\lim_{x \to 2}{h(x)} = 3 \text{however} h(2)\neq 3.\\
c) &\lim_{x \to 0}{ f( x)} \text{does not exist, however} f( 0) = 2.
\end{align*}
Tags: continuity, abstract-function, sketching, qualitative, v--g, a--g, t1, c2
My experience has been that students come to calculus with a lot of experience graphing functions that have a defining expression. However, asking them to draw a function - only given a few conditions and no defining expression - requires them to stretch their imagination. Sometimes I draw an example for someone in the class if they’re having trouble getting started - I try to make it wild to get their imagination going.
– James Epperson 1998-08-09