Unit 13 Honors / Extended Practice

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Honors / Extended pathway

Power Series, Taylor Series & Modelling Capstone

Deeper proof, synthesis, parameter analysis, and unfamiliar applications.

1. Find the radius of Σx^n/3^n.

2. Which statement best describes the central reasoning in Power Series & Radius of Convergence?

3. Find interval for Σ(x−2)^n/n.

4. Which statement best describes the central reasoning in Endpoint Testing & Interval of Convergence?

5. From 1/(1−x)=Σx^n, derive a series for 1/(1−x)².

6. Which statement best describes the central reasoning in Operations on Power Series?

7. Find the degree-3 Maclaurin polynomial for e^x.

8. Which statement best describes the central reasoning in Taylor Polynomials & Local Approximation?

9. Write four nonzero terms of cos x.

10. Which statement best describes the central reasoning in Benchmark Maclaurin Series?

11. Bound the error of 1+x+x²/2 approximating e^x at x=.1 using M=e^{.1}.

12. Which statement best describes the central reasoning in Taylor Remainder & Error Bounds?

13. Approximate ∫₀^{.5}e^{-x²}dx using terms through x⁴ in e^{-x²}.

14. Which statement best describes the central reasoning in Series in Integration & Differential Equations?

15. Name four required elements of the capstone defense.

16. Which statement best describes the central reasoning in Capstone Synthesis, Oral Defense & Calculus III Bridge?

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