Taylor Series Chapter Exam

Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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Question 1 1. What is the center of the following power series?

Question 2 2. Find the radius of convergence for the following power series.

Question 3 3. You're told that the radius of convergence for a given power series is (-7,5). What is the center of the power series?

Question 4 4. Which of these is another way to write the following function?

Question 5 5. The region of convergence for functions of a complex variable are defined by _____.

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Question 6 6. We can approximate a function of a complex variable using a Taylor series if we evaluate the series within the _____.

Question 7 7. Taking the derivative of u(x,y) with respect to x is an example of a _____.

Question 8 8. When discussing the Taylor series for functions of a complex variable, an analytic function is _____.

Question 9 9. The limit of 1/(n+2) as n goes to infinity is _____.

Question 10 10. Express the following as an interval:

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Question 11 11. 1 - 1/2 + 1/3 - 1/4 + ... is called a/an _____.

Question 12 12. If the ratio test produces a number less than 1, the infinite series _____.

Question 13 13. Which of the following functions has a finite Maclaurin series?

Question 14 14. Which of the following functions can also be written using summation notation?

Question 15 15. For the Maclaurin series, at what point do you evaluate your function and its derivatives?

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Question 16 16. What is the first term of the Maclaurin series?

Question 17 17. x5 for x = 2.02 is 2.025, which is 33.63 (to four significant figures). The first two terms of the Taylor series approximation to f(x) = x5 is a5 + 5a4 (x - a). Evaluating the first two terms of the Taylor series at x = 2.02 about the point a = 2 gives _____.

Question 18 18. The Taylor series is most accurate:

Question 19 19. Let's say you want to write the Taylor series for f(x) = ex. The first term is _____.

Question 20 20. To get a good approximation of f(x) for some value of x, choose a to be _____.

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Question 21 21. What is the center of the series below?

Question 22 22. What is the center of the series below?

Question 23 23. Which of the following is NOT a power series?

Question 24 24. What is a power series?

Question 25 25. What is 3 divided by the factorial of 3?

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Question 26 26. The first three terms of the MacLaurin series for f(x) = 1/(1 - x) is given by f(x) = 1 + x + x^2. Compare these two expression for f(x) at x equal to 0.2 ?

Question 27 27. The derivative of e^(2x) is 2e^(2x). What are the first two terms of the Taylor series for f(x) = e^(2x)?

Question 28 28. The first two terms of the Taylor series for e^x is e^a + (x - a)e^a. What are the first two terms of the corresponding MacLaurin series (note that e^0 = 1)?

Question 29 29. Find the radius of convergence for the following power series.

Question 30 30. If a function satisfies the two Cauchy-Riemann equations, then this function is _____.

Taylor Series Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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