How do you use a graphing calculator to find the limit of #xabs(x-4)# as x approaches -1?

Answer 1

-5

Use your calculator (or other graphing software/app) to plot the graph, then look to see what happens at #x=-1#

graph{x|x-4| [-10, 10, -5, 5]}

In this case, If #f(x)= x|x-4|#, then as #f(x)# is continuous, the limit is #f(-1)=-5#
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Answer 2

To use a graphing calculator to find the limit of x|abs(x-4)| as x approaches -1, follow these steps:

  1. Turn on your graphing calculator and enter the function: y = x|abs(x-4)|.

  2. Set the viewing window to include the x-value of -1. Adjust the window to show a range of x-values around -1 to observe the behavior of the function.

  3. Use the calculator's graphing feature to plot the function on the screen.

  4. Locate the point on the graph where x = -1. This is the point where x approaches -1.

  5. Observe the behavior of the graph as x approaches -1 from both sides (left and right). Check if the y-values are approaching a specific value or if there is a discontinuity.

  6. If the y-values approach a specific value as x approaches -1 from both sides, then that value is the limit. If the y-values do not approach a specific value or if there is a discontinuity, then the limit does not exist.

  7. Use the calculator's trace or table feature to examine the y-values as x gets closer to -1 to confirm the limit.

Remember, graphing calculators can provide visual representations of functions, but they may not always give precise numerical values for limits.

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Answer from HIX Tutor

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.

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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