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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.