What value does f(x) approach as x approaches infinity?
1. A hyperbola
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 this as
In this example, we can also say that
because the function also approaches 0 as you head towards negative infinity.
2. Asymmetric hyperbola
Select the second example. In this example, the limit at positive
infinity is different from the limit at negative infinity.
3. A line
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.
4. A sine curve
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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Other differentiation topics
Acknowledgements
Derived from the work of Thomas S. Downey under a Creative Commons Attribution 3.0 License.
