A limit curve is a visual way of representing a function's limit.
Within mathematics (specifically calculus), the concept of a "limit" refers to the maximum value any function y = f(x) can reach as x approaches a specific value. Take, for example, the function y = x^2. As x approaches infinity -- in other words, the values of x you plug into the equation become boundlessly large -- the limit of the function is also infinity, since y is always x times itself. Another way to represent limits is visually, in the form of "limit curves."
Instructions
1. Determine the function's limit before you set pencil to paper. If your function is y = 1/x, for example, and you want to find the limit as x approaches infinity, plug increasingly large values into the function until you begin to notice a pattern. For this example, use the values 1, 10, 150 and 1,000. Computing them as follows:
1/1 = 1
1/10 = .10
1/150 = .0076
1/1000 = .0001
You can see that as x gets larger (and approaches infinity), the function's value approaches zero. In this case, also note that when you plug in numbers smaller than one (.25, .01 and .005, for instance), the values of the function become progressively higher: 4, 10, and 500, respectively.
2. Plot points on a blank coordinate plane reflecting your function, keeping in mind that you should focus only on those within a manageable range. If, for example, your graph extends to the x coordinate of five, plug integers one through five into your function as follows:
1/1 = 1
1/2 = .5
1/3 = .33
1/4 = .25
1/5 = .20
and plot the resultant coordinates: (1,1); (2, .5); (3, .33); (4, .25); (5, .20) on your plane. For good measure, plot a single coordinate less than one (for example (.25, 4)) so you can get an idea of the shape of the curve.
3. Connect the dots, keeping in mind (if it isn't obvious from the coordinates) that your graph should have a curved shape. For the example function y = 1/x, keep in mind that the curve will approach (but never touch) the horizontal x-axis (in other words, the y coordinate of zero) as it moves rightward and extend infinitely upward as it reaches back toward the y-axis. You have now drawn a limit curve.
Tags: approaches infinity, your function, example function, function limit, keeping mind, limit curve