Limit Simulator

Approach a point from both sides to find limits

Grades 11–12

Function

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

Removable discontinuity at x = 1; simplifies to x + 1

Algebraic simplification:

\frac{x^2-1}{x-1} = \frac{(x+1)(x-1)}{x-1} = x+1 \quad (x \neq 1)

Removable discontinuity at x = 1; the limit still exists = 2

x approaches (a =)

x (from left)	f(x)	x (from right)	f(x)
0.9000	1.900000	1.1000	2.100000
0.9900	1.990000	1.0100	2.010000
0.9990	1.999000	1.0010	2.001000
0.9999	1.999900	1.0001	2.000100

Left limit ≈ 1.999900 = Right limit ≈ 2.000100
→ Limit exists:

\lim_{x \to 1} f(x) = 1.999900

Graph near x = 1