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

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

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

You click on the graph and zoom in and out.

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

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

- Turn on the graphing calculator and enter the function as (12(sqrt(x)-3))/(x-9).
- Go to the graphing mode or function plotter on the calculator.
- Set the window or range of x-values to include values close to 0, such as -0.1 to 0.1.
- Graph the function on the calculator.
- Look at the graph and observe the behavior of the function as x approaches 0.
- 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.
- 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.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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