57 lines
1.5 KiB
Markdown
57 lines
1.5 KiB
Markdown
---
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id: act-01-limits-and-derivatives-understanding
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title: "Unit 01 — Limits and Derivatives"
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mode: understanding
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open_at: "2026-02-01T00:00:00+01:00"
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close_at: "2026-12-31T23:59:59+01:00"
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retakes_enabled: true
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max_attempts: 999
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grade_max: 100
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---
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# Unit 01 — Limits and Derivatives
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## T1
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Type: essay
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Points: 20
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Prompt: Explain in your own words what a limit means and how it is used to define the derivative.
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Refs:
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- mat-01-limits-continuity#what-is-a-limit
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- mat-02-derivatives#derivative-definition
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Rubric:
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- Clear conceptual explanation (10)
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- Mentions difference quotient and limiting process (10)
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## T2
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Type: essay
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Points: 25
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Prompt: Compute the limit of (sin x)/x as x approaches 0 and briefly justify your result.
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Refs:
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- mat-01-limits-continuity#special-limits
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Rubric:
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- Correct limit value (15)
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- Justification is mathematically coherent (10)
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## T3
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Type: essay
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Points: 30
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Prompt: Differentiate f(x)=x^3-2x+sin x and simplify the result.
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Refs:
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- mat-02-derivatives#derivative-rules
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- mat-02-derivatives#derivatives-of-common-functions
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Rubric:
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- Applies power rule correctly (15)
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- Differentiates sin x correctly (10)
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- Simplifies correctly (5)
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## T4
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Type: file
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Points: 25
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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.
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Refs:
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- mat-02-derivatives#tangent-line-approximation
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Rubric:
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- Script runs and prints a numeric result (10)
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- Uses finite difference correctly (10)
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- Code is readable (5)
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