calculus/activities/01-limits-and-derivatives-understanding.md

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