How do you use a graphing calculator to find the limit of #x^2-5x# as x approaches 5?

Answer 1

You simply plot the graph (as below) and look to see if the function is "well behaved" (ie no discontinuities etc.) at the value you are interested. E.g.

E.g. A "well behaved " function #f(x)=x^2-5x# whose limit at #x=5# clearly exists and so #lim_(x rarr 5)x^2-5x=f(5)=0# graph{x^2-5x [-10, 10, -5, 5]}
Compared to #f(x)=1/(1-x)# which is infinite when x=1 and so #lim_(x rarr 1)1/(1-x)=oo# as #f(1)# is not defined graph{1/(1-x) [-10, 10, -5, 5]}
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Answer 2

To find the limit of x^2-5x as x approaches 5 using a graphing calculator, follow these steps:

  1. Turn on the graphing calculator and enter the function as y = x^2-5x.
  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 5, such as x-values from 4.9 to 5.1.
  4. Graph the function on the calculator.
  5. Look at the graph and observe the behavior of the function as x approaches 5.
  6. If the graph approaches a specific y-value as x gets closer to 5, then that y-value is the limit of the function as x approaches 5.
  7. If the graph does not approach a specific y-value and instead becomes undefined or approaches infinity, then the limit does not exist.

Note: It is important to ensure that the calculator is set to the appropriate mode (degrees or radians) and that the function is entered correctly to obtain accurate results.

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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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