Let $ f( x) = \frac{1}{ x}\sin x$, assume we only take $x>0$.
- Sketch the graph of $ f( x)$.
- Find $\lim_{x \to 0} { f( x)}$ and $\lim_{t\to 0} f( {\frac{1}{ t}})$.
Tags: limits, limits-at-infinity, trig, rational, sketching, classic, computation, a--a, a--g, t2, c3
At this point, students have had chances to draw rough sketches of functions and to think about general behavior of functions commonly encountered in high school mathematics Asking them to graph f(x)= (sin x)/ x stimulates good discussion about the features of the graph. It is helpful to go around to each group and ask questions about their graphical interpretations. In part b, I want them to refine the condition - that is, “hey, we can only look at x->0 from the right because f(x) isn’t defined for x<0.”
– James Epperson 1998-08-09