Limit Calculator
Evaluate the limit of f(x) as x approaches a value by numerical approximation from both sides.
Inputs
Enter function using x.
Limit
1.0000000000
Left limit (x→a⁻)
1.0000000000
Right limit (x→a⁺)
1.0000000000
Status
Two-sided limit exists
Step by step
Values used
f(x) = sin(x)/x; x approaches = 0
Numerical limit
lim(x→a) f(x) ≈ f(a ± h) as h → 0
Limit
= 1.0000000000
Left limit (x→a⁻)
= 1.0000000000
Right limit (x→a⁺)
= 1.0000000000
Status
= Two-sided limit exists
How it works
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.
Formula
Numerical limit
lim(x→a) f(x) ≈ f(a ± h) as h → 0
- a
- Approach point
- h
- Decreasing step sizes from 1e-2 to 1e-8
Frequently Asked Questions
What if the limit does not exist?
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.
Can I find limits at infinity?
Enter a large value like 1000000 for x approaches. The calculator evaluates from both sides of that point.