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continuity

Verify function continuity by checking definitions, computing limits with SymPy, and proving properties via Z3.

8|1|Updated Jan 4, 2026
Search Tags:#limits#real analysis#calculus#continuity#z3#sympy
One-click install
npx skills add https://github.com/scooter-lacroix/Maestro --skill continuity-scooter-lacroix
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: continuity
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/real-analysis/continuity
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill continuity-scooter-lacroix

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes scripts (resource) and references (resource) components.

What problem does it solve?

This skill provides a structured approach to solving problems related to the continuity of functions in real analysis.

Core Features & Use Cases

  • Definition Verification: Checks if a function meets the three conditions for continuity at a point.
  • Limit Computation: Utilizes SymPy to symbolically compute limits, including one-sided limits.
  • Formal Proof Assistance: Integrates with Z3 to assist in proving continuity properties.
  • Use Case: Determine if the function f(x) = (x^2 - 1) / (x - 1) is continuous at x = 1.

Quick Start

Use the continuity skill to check if the function f(x) is continuous at point a.

Frequently Asked Questions about continuity

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I check if a function is continuous at a specific point in real analysis?▼

To check function continuity at a point, verify the three continuity conditions using real analysis strategies. This skill evaluates the function definition and computes limits to determine if the function is continuous at the specified point.

How do I compute one-sided limits for continuity verification using SymPy?▼

You can compute one-sided limits for continuity verification using SymPy. This skill utilizes the SymPy library to symbolically calculate both standard and one-sided limits required to verify continuity conditions.

Can I use Z3 to formally prove continuity properties of a function?▼

Yes, you can use Z3 to assist with formal proofs of continuity properties. This skill integrates the Z3 library to help construct and verify formal proofs for real analysis continuity problems.

Do I need Python with SymPy and Z3 installed to analyze function continuity?▼

Yes, you need a Python environment with SymPy and Z3 libraries installed to analyze function continuity. These dependencies are required for symbolic limit computation and formal proof assistance.

What is the best way to determine if a piecewise function is continuous?▼

The best way to determine if a piecewise function is continuous is by verifying its definition and computing limits at boundary points. This skill checks continuity conditions and uses SymPy to handle limit calculations.

Why does my function limit computation fail when checking continuity at a removable discontinuity?▼

Function limit computation may fail at a removable discontinuity if the function is undefined at that point. This skill addresses such continuity problems by evaluating the definition and computing limits around the discontinuity.

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