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From Secant to Tangent

Secants collapsing into a local slope · BC Calculus · greeting

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Owl · Mock interview — From Secant to Tangent. I ask; you answer.

Owl · We're inventing a local slope by limiting a family of secants. What do you expect those secant slopes to do as the second point approaches the first?

Larry’s gold answer — Show text to read it out loud.

Larry · gold answer · I expect the secant slopes to settle toward one number — the local climb rate at mile 1.4 — if the trail is smooth there.

Owl: We're inventing a local slope by limiting a family of secants. What do you expect those secant slopes to do as the second point approaches the first?

You: —