Graphically Exploring Limits

What is the limit of f as x approaches 5 from the left?

You can drag the gray dot, x-value, on the x-axis. [br]1. Drag the x-value so that it is approaching 5 from the left, or from the negative side. [br]2. Watch the values of f(x) = y as you slide the x-value towards 5 from the left. [br](DON'T LET THE GRAY DOT TOUCH x = 5, but get as close as you can)[br]3. This is the limit of f(x) as x approaches 5 from the left: [math]\lim_{x\to5^-}f\left(x\right)[/math]

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What is the limit of f as x approaches 5 from the right?

1. Drag the x-value so that it is approaching 5 from the right, or from the positive side. [br]2. Watch the values of f(x) = y as you slide the x-value towards 5 from the right. [br](DON'T LET THE GRAY DOT TOUCH x = 5, but get as close as you can)[br]3. This is the limit of f(x) as x approaches 5 from the left: [math]\lim_{x\to5^+}f\left(x\right)[/math]

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What is f(5)?

Enter 5 into the box labeled "x = ", you will see the value of f(x) at x = 5.

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Check for Understanding

Question 1

What is [math]\lim_{x\to5^-}f\left(x\right)[/math]?

Question 2

What is [math]\lim_{x\to5^+}f\left(x\right)[/math]?

Question 3

What is [math]\lim_{x\to5^{ }}f\left(x\right)[/math]?

Question 4

What is [math]f\left(5\right)[/math]?