Question Open a trail map of elevation versus distance. Pick a point at mile 1.4 where the path is curving. Draw a chord from that point to mile 1.9 — that's a secant, and its slope is an average climb rate. Now slide the second point closer: 1.7, 1.55, 1.42… Each new chord is still a secant, but the second foot is creeping toward the first.
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Describe the tangent as the limiting position of secants Compute numerical slopes for a sequence of smaller h Use limit language for slope at a point Reject the myth that a tangent must meet the curve only once
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Elevation vs distance Anchor at mi 1.4 Secants to 1.9, 1.7, 1.55… Zoom in → curve ≈ line?
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