Evaluate the limit of f(x) as x approaches a value by numerical approximation from both sides.
Evaluates lim(x→a) f(x) numerically by computing f(a±h) for progressively smaller h values and checking if the left and right limits converge to the same value. If they agree within tolerance, the two-sided limit exists. Otherwise, the one-sided limits are reported separately.
Numerical limit
lim(x→a) f(x) ≈ f(a ± h) as h → 0
If the left and right limits differ, the two-sided limit does not exist. Both one-sided values are reported so you can see the discontinuity.
Enter a large value like 1000000 for x approaches. The calculator evaluates from both sides of that point.