Subject: Calculus

Find lim x→1 (x² − 1)/(x − 1)

A removable discontinuity — factor and simplify, or sample both sides.

Answer lim x→1 ≈ 2

Solution

Limit lim x→1 of (x^2 - 1) / (x - 1)
x = 0.99999 f(x) = 1.99999
x = 0.9999 f(x) = 1.9999
x = 0.999 f(x) = 1.999
x = 0.99 f(x) = 1.99
x = 0.9 f(x) = 1.9
x = 1.1 f(x) = 2.1
x = 1.01 f(x) = 2.01
x = 1.001 f(x) = 2.001
x = 1.0001 f(x) = 2.0001
x = 1.00001 f(x) = 2.00001
Left side x→1⁻ f(x) → 2
Right side x→1⁺ f(x) → 2
Conclusion Both sides agree → limit ≈ 2

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