Pythos Oracle

AI Calculus Tutor & Problem Solver

Explore limits, differentiation rules, integration techniques, and differential equations with verified Socratic rigor.

Mastering Calculus with Verified AI Guidance

Calculus connects algebra and geometry through change and accumulation. Pythos helps you master both computational techniques (power rule, product rule, u-substitution, integration by parts) and foundational proofs (the Fundamental Theorem of Calculus, tangent slopes, optimization bounds). Every derivation and step is deterministically checked by our SymPy computer algebra engine and the proprietary Pythos verifier before presentation.

Core Calculus Disciplines

✦ Limits & Continuity

Evaluate limits as $x \to c$ or $x \to \infty$, apply L'Hôpital's Rule for $\frac{0}{0}$ and $\frac{\infty}{\infty}$, and examine continuity intervals.

✦ Derivatives & Optimization

Differentiate polynomials, trigonometric curves, and exponentials using chain, product, and quotient rules. Solve applied optimization problems.

✦ Definite & Indefinite Integrals

Compute enclosed areas, evaluate antiderivatives, and perform integration by parts: $$\int u \, dv = uv - \int v \, du$$

✦ Differential Equations

Solve separable first-order differential equations and model physical growth, cooling, velocity decay, and harmonic systems.

Sample Calculus Problems for Pythos

Ask Pythos questions directly or test derivations:

"What is the derivative of $f(x) = x^3 \sin(x)$ using the product rule?"
"Evaluate the fundamental limit: $\lim_{x \to 0} \frac{\sin(x)}{x}$ with proof."
"How do I evaluate $\int x e^x \, dx$ using integration by parts?"
"Find the local extrema and inflection points of $y = x^3 - 3x$."
Practice Calculus in Pythos