Approximation audit
Produce one small report using your lab code and retained outputs, plus an independent changed case. Reuse this report as the semester calculus appendix.
Required evidence
- Explain the contracts and error assumptions of all three algorithms. Include a hand derivation of central-difference order, the trapezoid error bound for x² and the root bracket width after k halvings.
- Keep the derivative step-size experiment and describe what actually happened. Distinguish cancellation from analytic truncation error.
- Audit the rate-2 exponential model: prove normalization and mean, choose cutoff and grid count for total mass error below 0.001 using separate tail and quadrature bounds, and compare to exact finite-interval mass. The provided cutoff 5 and n=300 give a starting calibration; choose and defend a different pair.
- Change the rate to 3. Predict a cutoff and sufficient n before running. Use |f″|≤27 on the nonnegative interval. A valid example is cutoff 3 and n=300: tail exp(−9) plus 27·27/(12·300²) is below 0.001. Your reasoning must connect rate units to time units.
- Include one invalid bracket, one budget failure and one changed root function with a known answer. Explain why a passing result does not establish that an exponential model describes a real service latency distribution.
Handoff
Deliver the code, exact calculations, actual output files, environment/run instructions, source sections, help declaration and a short account of an error you repaired. A screenshot alone is insufficient. Reproduce a selected calculation without the reference implementation or generated code. Score using CAL7 and preserve CAL1–CAL6 reasoning separately.