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.
Other differentiation topics
Acknowledgements
Derived from the work of Thomas S. Downey under a Creative Commons Attribution 3.0 License.
