# Taylor Series Chapter Exam

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### Page 1

#### Question 1 1. Express the following as an interval:

#### Question 2 2. If the ratio test produces a number less than 1, the infinite series _____.

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Question 3
3.
The limit of 1/(*n*+2) as *n* goes to infinity is _____.

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

#### Question 5 5. Which of the following functions has a finite Maclaurin series?

### Page 2

#### Question 6 6. Which of the following functions can also be written using summation notation?

#### Question 7 7. For the Maclaurin series, at what point do you evaluate your function and its derivatives?

#### Question 8 8. What is the first term of the Maclaurin series?

#### Question 9 9. What is a power series?

#### Question 10 10. What types of functions can be represented by a power series?

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#### Question 11 11. What is the center of the series below?

#### Question 12 12. Which of the following is NOT a power series?

#### Question 13 13. Which of these is another way to write the following function?

#### Question 14 14. Find the radius of convergence for the following power series.

#### Question 15 15. You're told that the radius of convergence for a given power series is (-7,5). What is the center of the power series?

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#### Question 16 16. Find the radius of convergence for the following power series.

#### Question 17 17. What is 3 divided by the factorial of 3?

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Question 18
18.
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)?

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Question 19
19.
The derivative of *e*^(2*x*) is 2*e*^(2*x*). What are the first two terms of the Taylor series for *f*(*x*) = *e*^(2*x*)?

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Question 20
20.
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 ?

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#### Question 21 21. We can approximate a function of a complex variable using a Taylor series if we evaluate the series within the _____.

#### Question 22 22. If a function satisfies the two Cauchy-Riemann equations, then this function is _____.

#### Question 23 23. The region of convergence for functions of a complex variable are defined by _____.

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Question 24
24.
Taking the derivative of *u*(*x*,*y*) with respect to *x* is an example of a _____.

#### Question 25 25. The Taylor series is most accurate:

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Question 26
26.
You are asked to write the first two terms of the Taylor series for *f*(*x*) = sin *x*. Your result is _____.

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Question 27
27.
Let's say you want to write the Taylor series for *f*(*x*) = *e**x*. The first term is _____.

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Question 28
28.
To get a good approximation of *f*(*x*) for some value of *x*, choose *a* to be _____.

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Question 29
29.
The interval of convergence for a power series in *x* refers to the values of:

#### Question 30 30. The Maclaurin series is a special case of which of these series?

#### 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!