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Limits

Where is f(x) heading as x closes in on a point? Walk in from both sides, meet a hole, a jump and an asymptote, then pin "close" down with an ε–δ band.

Removable hole · step 1 of 39

Speed

A limit asks where f(x) is heading as x gets close to a — not what f(a) happens to be. Here a = 1. We will walk towards it from the left and from the right, three different ways.

f(x) = \dfrac{x^2 - 1}{x - 1}

Limits

Where is f(x) heading as x closes in on a point? Walk in from both sides, meet a hole, a jump and an asymptote, then pin "close" down with an ε–δ band.

Removable hole · step 1 of 39

Speed

A limit asks where f(x) is heading as x gets close to a — not what f(a) happens to be. Here a = 1. We will walk towards it from the left and from the right, three different ways.

f(x) = \dfrac{x^2 - 1}{x - 1}

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Limits

See also

Limits

See also