Calculadora de Limite (numérico)

This calculator numerically approximates the limit of a real function as x approaches a specific value a. It handles expressions like sin(x)/x, (1+1/x)^x, or any user-defined continuous function. The calculation evaluates the function at points very close to a, using a small step (h = 1e-7) from both left and right sides, then averages the two results. This provides an accurate estimate of the limit, useful for understanding function behavior near a point.

You can use this tool to verify classic calculus limits, such as the fundamental limit sin(x)/x as x→0 (which is 1) or the limit defining Euler's number (1+1/x)^x as x→∞. It is also helpful for exploring one-sided limits and checking continuity at a point. Simply input the function expression and the value a that x approaches. The calculator returns an approximate limit value, indicating whether it exists or diverges.

Important caveats: numerical approximation may fail if the function has discontinuities or rapid oscillations near the point. The fixed step h=1e-7 may not be suitable for functions that change abruptly. Limits at infinity (x→∞) are not directly handled; use a large value for a, but note that precision may be limited. Always interpret results cautiously and, if possible, confirm with analytical methods.