---
id: act-01-limits-and-derivatives-understanding
title: "Unit 01 — Limits and Derivatives"
mode: understanding
open_at: "2026-02-01T00:00:00+01:00"
close_at: "2026-12-31T23:59:59+01:00"
retakes_enabled: true
max_attempts: 999
grade_max: 100
---

# Unit 01 — Limits and Derivatives

## T1
Type: essay
Points: 20
Prompt: Explain in your own words what a limit means and how it is used to define the derivative.
Refs:
- mat-01-limits-continuity#what-is-a-limit
- mat-02-derivatives#derivative-definition
Rubric:
- Clear conceptual explanation (10)
- Mentions difference quotient and limiting process (10)

## T2
Type: essay
Points: 25
Prompt: Compute the limit of (sin x)/x as x approaches 0 and briefly justify your result.
Refs:
- mat-01-limits-continuity#special-limits
Rubric:
- Correct limit value (15)
- Justification is mathematically coherent (10)

## T3
Type: essay
Points: 30
Prompt: Differentiate f(x)=x^3-2x+sin x and simplify the result.
Refs:
- mat-02-derivatives#derivative-rules
- mat-02-derivatives#derivatives-of-common-functions
Rubric:
- Applies power rule correctly (15)
- Differentiates sin x correctly (10)
- Simplifies correctly (5)

## T4
Type: file
Points: 25
Prompt: Create a small Python script @solutions/numerical_derivative.py that approximates the derivative using a finite difference and prints the approximate derivative of x^3 at x=2 with step h=1e-5.
Refs:
- mat-02-derivatives#tangent-line-approximation
Rubric:
- Script runs and prints a numeric result (10)
- Uses finite difference correctly (10)
- Code is readable (5)