This calculator bundles direct substitution checks, Richardson-based numeric L'Hôpital, one-sided sampling, and a graph centred on the approach point. کاپی کریں the قابلِ شیئر URL, LaTeX summary, or CSV table for lesson handouts.
Beyond polynomials and trigonometric functions, you can call abs, sgn, sqrt, and constants such as pi, +inf, and -inf.
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How does the numeric L'Hôpital routine work?
Whenever both numerator and denominator approach 0 or ∞, the calculator estimates derivatives with Richardson extrapolation, applies L'Hôpital's rule up to six times, and records each attempt in the step log.
How are one-sided limits visualised?
Samples at 10-1 to 10-6 from the approach point appear in the table and in the graph. If the sides disagree we highlight that only a one-sided limit exists.