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

1 Answer
Dec 23, 2016

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]}