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Limit calculator
Limit calculator
Enter your values below and press Calculate to see your result instantly.
Convergence Target: limit as x → a
lim
Target "a"
Standard Polynomial Function: f(x) = Ax² + Bx + C
x² +
x +
The Converged Output Limit (L)
7.000
LHL: LEFT-HAND TRAJECTORY (-0.001)
6.992
RHL: RIGHT-HAND TRAJECTORY (+0.001)
7.008
Calculations complete.
About the Limit calculator
Find the limit of a quadratic function as x approaches a value, checking both the left-hand and right-hand approach.
How to use the Limit calculator
- Enter the coefficients Scale (A), Linear (B) and Constant (C) of f(x) = Ax² + Bx + C.
- Enter the target value a for the limit as x → a.
- Press the calculate button to see the left-hand limit, the right-hand limit and the converged value.
Formula and method
The limit of f(x) as x approaches a exists if the values from the left and right approach the same number. For polynomials it equals f(a).
Worked example
For f(x) = x² + 2x + 1 as x → 2, the limit is 9.
Tips
- Polynomials are continuous, so their limits equal their values.
- If the left and right limits differ, the limit does not exist.
Frequently Asked Questions
The value the function approaches as x comes from just one side of the target.