Free AI Calculus Tutor & Problem Solver

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).

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