In this chapter we have learned how [b]limits[/b] are a way of investigating functions. Specifically, we've seen that limits can give us insight into the growth rate of a function at a point.[br][br]We looked at two functions, [code]f(x)=x^2+2*x[/code], and [code]g(x)[/code], our model of the height of a missile over time from [url=https://www.geogebra.org/m/x39ys4d7#material/aayx7rmz]earlier in the book[/url]. In both cases, we investigated how the slope of secant lines limits towards the growth rate of the function at a point. [br][br]The most important outcome of our study is that we came up with a process (albeit a clunky one) for calculating the growth rate of functions. To recap, the process is:[br][br][list][*]Plot a point on the function, usually called [code]A[/code][/*][*]create a "dummy" variable [code]h[/code] set to a small number[/*][*]plot a second point on the function close to [code]A[/code] by "nudging" the x-coordinate of [code]A[/code] with [code]h[/code][/*][*]create the so-called "secant line" between the two points[/*][*]study the limit of the slopes of the secant lines when [code]h[/code] trends towards 0[/*][/list][br]At the end of this process we arrive at a number: the limit of the slope of the secant lines as h tends to 0.[br][br]As we'll see in the next chapter, this number represents the growth rate of the function at the point [code]A[/code].[br][br]This growth rate of the function at a point is extremely important in calculus, and it has two other names: the [b]derivative[/b] of [code]f[/code] at [code]A[/code]; the [b]instantaneous rate of change[/b] of [code]f[/code] at [code]A[/code]. We'll study this concept at length, and refine our clunky process in the next chapter.[br][br]Side-note: If you're curious in some of the other uses for limits aside from derivatives, check out [url=https://www.geogebra.org/m/x39ys4d7#material/rfyyq8ah]this Geogebra activity[/url] in the Miscellany chapter at the end of this book