2. Template by Bill Arcuri, WCSD Who Wants to Be a Millionaire?

3. Taylor and Maclaurin Series By: Rachel Hay and Daniel Mai _________________________ _____________________ ___________________ __________________ _________________ ______________ Click the appropriate dollar amount at right to proceed to the question

4. Template by Bill Arcuri, WCSD Phone A Friend “OK Contestant…Please select a friend to help you with this one. You have thirty seconds to discuss your options…” Return to the Question

5. Template by Bill Arcuri, WCSD Ask the Audience “Audience, we need your help on this one…in a moment, we’ll ask you to indicate, by show of hands, your choice for the correct answer…” Return to the Question

6. Template by Bill Arcuri, WCSD Fifty - Fifty You’ve asked that two of the wrong answers be eliminated, leaving you with one wrong answer plus the correct one. 50/50 Return to the Question

7. Template by Bill Arcuri, WCSD Correct Correct! Proceed to Next Question

8. Template by Bill Arcuri, WCSD Incorrect Sorry, That’s Incorrect Return to the Question

9. Template by Bill Arcuri, WCSD 1 Maclaurin series is a Taylor series centered at: 02 50/50 A CD B

10. Template by Bill Arcuri, WCSD Nth root test Which test is used to determine the interval of convergence of a Taylor series? Nth term testLimit comparison test Ratio Test A CD B 50/50

11. Template by Bill Arcuri, WCSD Equal to ½ the interval of convergence The radius of convergence is… Unable to be determined Equal to ¼ the interval of convergence Always equal to 1 A CD B 50/50

12. Template by Bill Arcuri, WCSD The Taylor series for f(x) centered at a has which form? A CD B 50/50

13. Template by Bill Arcuri, WCSD The first term of the series The error of a truncated Taylor series is less than: The first term before the cut off None of these The next term after the cut off A CD B 50/50

14. Template by Bill Arcuri, WCSD sometimes have the same radius of convergence Integrals and derivatives of Taylor series… always have the same radius of convergence never have the same radius of convergence always have different radii of convergence A CD B 50/50

15. Template by Bill Arcuri, WCSD sometimes have the same interval of convergence Integrals and derivatives of Taylor series… always have the same interval of convergence never have the same interval of convergence always have different intervals of convergence A CD B 50/50

16. Template by Bill Arcuri, WCSD Sin(x) ∞ ∑ x n /n! represents which series? N=0 Cos(x)exex ln(1-x) A CD B 50/50

17. Template by Bill Arcuri, WCSD Sin(x) Which of these series is NOT alternating? Cos(x)exex ln(x) A CD B 50/50

18. Template by Bill Arcuri, WCSD 1/(1-x) These terms represent the first four terms of which series? x - x 3 /3! + x 5 /5! – x 7 /7! Sin(x)ln(1-x) Cos(x) A CD B 50/50

19. Template by Bill Arcuri, WCSD Sin(x) These terms represent the first four terms of which series: (x-1) – (x-1) 2 /2 + (x-1) 3 /3! – (x-1) 4 /4! Cos(x)exex ln(x) A CD B 50/50

20. Template by Bill Arcuri, WCSD The series cos(x) has the form: A CD B 50/50

21. Template by Bill Arcuri, WCSD Cos(x) Which series remains the same after term by term differentiation? 1/(1-x) 2 exex Sin(x) A CD B 50/50

22. Template by Bill Arcuri, WCSD 1 + x/2 + x 2 /3! + x 3 /4! Given that the first four terms of the Maclaurin series expansion of e x : 1 + x + x 2 /2 + x 3 /3! Determine the Maclaurin expansion for (e x -1)/x. 2 + x/2 + x 2 /3! + x 3 /4! x/2 + x 2 /3! + x 3 /4! + x 4 /5! 1 + (x-1) + (x-1) 2 /2 + (x-1) 3 /3! A CD B 50/50

23. Template by Bill Arcuri, WCSD Cos(x) ∞ ∑ (2x)n / n! represents which series? N=0 ln(x)Sin(2x) e 2x A CD B 50/50