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Let's study the end behavior of the function . Look at the graph and table of values, and use the tool to explore the graph. What value does f(x) approach as x becomes large in absolute value?
As you can see from the graph and the table, as the absolute value of x increases, f(x) approaches 0.
Now let's look at the end behavior of other functions of the form . Use the tool to change the degree of x and notice how this affects the shape of the graph and the values in the table. You can adjust the window to explore the graph further.
What is the limit of as x approaches infinity? What is the limit as x approaches negative infinity? Click "Done Exploring" when finished.
You should have noticed that as x approaches positive or negative infinity, approaches zero.
You can use this fact to algebraically evaluate the limit of rational functions as x approaches infinity. Consider the function .
To find the limit of this function as x approaches infinity, first divide both the numerator and the denominator by the highest power of x that occurs in the function. You can assume that x ¹ 0 because we are only interested in very large values of x.
Now you can use the limit laws to simplify and find the limit.
Use the limit laws to find the indicated limits. Click "Submit" when finished.
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