Question

When should you use graphs to determine limits of functions?

Answer 1

Glib answer: When you have to.

Better answer:
1) When we do not have an expression fo `f(x)`, but only a graph.
2) When you, personally find it more clear.

Eventually, students have no trouble with finding `lim_(xrarr3)f(x)`
when `f(x)= 3x+2 if x<5`
and `f(x)=x^2-8 if x >=5`
without a graph.

To begin, most of us really need to think about the graph, either to get the correct answer, or to understand why `17` is the correct answer.

For some functions, the graph can "point us in the right direction". Fo r example: looking at the graph of `f(x)=sinx/x` makes us think that `lim_(xrarr0)sinx/s=1` .

But thinking it's true isn't the same as KNOWING it's true. So we still need to try to prove it.