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Lesson · What is a limit?

Some functions have a gap. Take

f(x)=x2−1x−1f(x) = \frac{x^2 - 1}{x - 1}

At x=1x = 1 you get 00\frac{0}{0}, which is undefined. But we can still ask: what does f(x)f(x) get close to as xx gets close to 11? Let's sneak up on it.

Evaluate f(0.99)f(0.99).

f(0.99)=0.992−10.99−1f(0.99) = \frac{0.99^2 - 1}{0.99 - 1}