Limits at Infinity
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We can also talk about what value f (x) approaches as x approaches infinity.
Try the following:
- The first graph shows a simple hyperbola. What is the limit when
? In other
words, what value does f (x) approach as x approaches infinity? Move the x slider so that x gets
bigger and bigger. As you will note, f (x) approaches 0 for
this example. We write infinity f(x) = 0" src="assets/images/Eqn7.gif" align="middle" />. In this case, we can also say that
-infinity f(x) = 0" src="assets/images/Eqn8.gif" align="middle" />, because the function also approaches 0 as you head towards negative infinity.
- Select the second example. In this example, the limit at positive
infinity is different from the limit at negative infinity.
- Select the third example. This is just a line. The limits at positive
and negative infinity do not exist, because the function's output just
keeps on getting bigger and bigger as x heads towards infinity.
You can zoom out multiple times to allow you to move the slider to bigger
and bigger values.
- Select the fourth example. This is just a sine curve. The limits at positive and negative infinity do not exist, because the function's output keeps oscillating up and down as bigger as x heads towards infinity. You can zoom out multiple times to allow you to move the slider to bigger and bigger values.
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© Copyright 2001 David J. Eck
© Copyright 2007 Thomas S. Downey
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