Question

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

Answer 1

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

Explanation:

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.