Question

How do you use a graphing calculator to find the limit of `x^2-5x` as x approaches 5?

Answer 1

You simply plot the graph (as below) and look to see if the function is "well behaved" (ie no discontinuities etc.) at the value you are interested. E.g.

Explanation:

E.g. A "well behaved " function `f(x)=x^2-5x` whose limit at `x=5` clearly exists and so `lim_(x rarr 5)x^2-5x=f(5)=0`
graph{x^2-5x [-10, 10, -5, 5]}

Compared to `f(x)=1/(1-x)` which is infinite when x=1 and so `lim_(x rarr 1)1/(1-x)=oo` as `f(1)` is not defined
graph{1/(1-x) [-10, 10, -5, 5]}