The code from the previous activity has created a second point just to the right of [code]A[/code] on the graph of [code]f(x)[/code]. The variable [code]h[/code] controls this second point by providing a "nudge" to the x coordinate of [code]A[/code]. If [code]h[/code] is positive, the new point is to the right of [code]A[/code]. If [code]h[/code] is negative, the new point is to the left. If [code]h[/code] is 0, the new point is the same as [code]A[/code]. [br][br]It's best to think of [code]h[/code] as providing a "small nudge" or "small difference" in the x-coordinate of [code]A[/code]. Indeed, some calculus books refer to [code]h[/code] as Δx ("Delta x"); the use of the Greek letter Δ ("Delta") is meant to invoke the idea of a [i]difference[/i] because the word "difference" starts with the letter "d". [br][br]Cool.[br][br]In my experience, I've found that when mathematicians use Greek letters, more confusion arises than clarity is produced, so I'll avoid using greek characters as best I can, and for now we'll just stick with [code]h[/code].[br][br]Use the line tool [icon]/images/ggb/toolbar/mode_join.png[/icon] to create the line between these two points. [br][br]If you have trouble selecting the two points, you can set [code]h[/code] to a larger value (0.3 for instance) to make it easier to click on them one at a time.[br][br]Once the line between the two points is created, move [code]h[/code], and notice that the line changes. You might notice that when [code]h[/code] is very close to 0, the slope of the line very closely matches the graph of [code]f(x)[/code]. If we think of [code]f(x)[/code] as "growing" from left to right, you might say that the line matches this growth. More on this in the next chapter.[br][br]However, also observe that when you set [code]h[/code] to 0, the line disappears! The reason is quite simple: you need two unique points to determine a line, and when [code]h[/code] is 0 the two points are not unique.

Move forward to see what this mysterious variable [code]h[/code] has to do with the [b]limit[/b] concept this chapter is supposed to be all about!