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

Question

Elijah Abram · Accepted Answer

# 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.

Charles Arocha · Answer

undefined To use a graphing calculator to find the limit of (12(sqrtx-3))/(x-9) as x approaches 0, follow these steps:

1. Turn on the graphing calculator and enter the function as (12(sqrt(x)-3))/(x-9).
2. Go to the graphing mode or function plotter on the calculator.
3. Set the window or range of x-values to include values close to 0, such as -0.1 to 0.1.
4. Graph the function on the calculator.
5. Look at the graph and observe the behavior of the function as x approaches 0.
6. The limit of the function as x approaches 0 can be determined by observing the y-values on the graph as x gets closer to 0.
7. The calculator may also have a built-in limit function or feature that can directly calculate the limit for you. Consult the calculator's manual or guide to find out if this feature is available and how to use it.

That's it! By following these steps, you can use a graphing calculator to find the limit of (12(sqrtx-3))/(x-9) as x approaches 0.