How do you use a graphing calculator to find the limit of ##(12(sqrtx-3))/(x-9)## as x approaches 0?

How do you use a graphing calculator to find the limit of ##(12(sqrtx-3))/(x-9)## as x approaches 0?

lim_(x rarr 0)(12(sqrtx-3))/(x-9) = 4

You can use any graphing program (eg Calculator, Autograph, Internet Sites) in the case I’ll use the built in Socratic graphing functionality:

Let ## y = (12(sqrtx-3))/(x-9) ##, Then we get the following graph:

graph{(12(sqrtx-3))/(x-9) [-10.07, 9.93, -2.58, 7.42]}

You click on the graph and zoom in and out.

If we zoom in on the point where the curve touches the ##y##-axis:

graph{(12(sqrtx-3))/(x-9) [-0.0533, 0.06627, 3.96395, 4.0237]}

it would appear that ## lim_(x rarr 0)(12(sqrtx-3))/(x-9) = 4 ##, and in fact this is the case.