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5. Determine whether the following series converge or diverge. Clearly state the test you are using and the evidence backing your conclusion. n a In n n n³+1 n=0 6. Given the power series 80 (3x - 2)" n42n n=1 a) Find the radius of convergence of the series. b) Find the interval of convergence of the series. (Do not forget to also check the endpoints of the interval of convergence of the series.) 7. a) Find the Maclaurin series of the function f(x) = 1 9+x² (Hint: It may be convenient for you to use the series for the function 1 1-u n=0 b) What is the radius of convergence of the Maclaurin series you found for f? 8. a) Find an equation for the tangent plane to the surface z = √³-2y³ at the point (1, 1,-1).. b) Find the distance of the point (-1,1,0) from the plane you found in a). 9. Let a = 27+-k, b = 5i - 3k, c=i-2j+ k, be three vectors in the 3-dimensional space. a) Find the area of the parallelogram with sides the vectors a and 6. b) Find the volume of the parallelepiped with sides the vectors a, b, and c. c) Find the angle between the vectors a and b. (You may leave your answer as 0 = cos ¹().) b) n=2

5. Determine whether the following series converge or diverge. Clearly state the test you are using and the evidence backing your conclusion. n a In n n n³+1 n=0 6. Given the power series 80 (3x - 2)" n42n n=1 a) Find the radius of convergence of the series. b) Find the interval of convergence of the series. (Do not forget to also check the endpoints of the interval of convergence of the series.) 7. a) Find the Maclaurin series of the function f(x) = 1 9+x² (Hint: It may be convenient for you to use the series for the function 1 1-u n=0 b) What is the radius of convergence of the Maclaurin series you found for f? 8. a) Find an equation for the tangent plane to the surface z = √³-2y³ at the point (1, 1,-1).. b) Find the distance of the point (-1,1,0) from the plane you found in a). 9. Let a = 27+-k, b = 5i - 3k, c=i-2j+ k, be three vectors in the 3-dimensional space. a) Find the area of the parallelogram with sides the vectors a and 6. b) Find the volume of the parallelepiped with sides the vectors a, b, and c. c) Find the angle between the vectors a and b. (You may leave your answer as 0 = cos ¹().) b) n=2

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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5. Determine whether the following series converge or diverge. Clearly state the test you are using and the evidence backing your conclusion. n a In n n=2 n n=0 7³ +1 6. Given the power series (3x - 2)" n42n n=1 a) Find the radius of convergence of the series. b) Find the interval of convergence of the series. (Do not forget to also check the endpoints of the interval of convergence of the series.) 7. a) Find the Maclaurin series of the function f(x) = 1 9+2² (Hint: It may be convenient for you to use the series for the function =Σu".) 1- u n=0 b) What is the radius of convergence of the Maclaurin series you found for f? 8. a) Find an equation for the tangent plane to the surface z = √√³ - 2y³ at the point (1,1,-1). b) Find the distance of the point (-1,1,0) from the plane you found in a). 9. Let a = 27+ 3 − k, b = 5ỉ – 3k, c = i − 2j+ k, be three vectors in the 3-dimensional space. a) Find the area of the parallelogram with sides the vectors a and 6. b) Find the volume of the parallelepiped with sides the vectors a, b, and c. c) Find the angle between the vectors a and b. (You may leave your answer as 0 = cos ¹().) b)
Transcribed Image Text:5. Determine whether the following series converge or diverge. Clearly state the test you are using and the evidence backing your conclusion. n a In n n=2 n n=0 7³ +1 6. Given the power series (3x - 2)" n42n n=1 a) Find the radius of convergence of the series. b) Find the interval of convergence of the series. (Do not forget to also check the endpoints of the interval of convergence of the series.) 7. a) Find the Maclaurin series of the function f(x) = 1 9+2² (Hint: It may be convenient for you to use the series for the function =Σu".) 1- u n=0 b) What is the radius of convergence of the Maclaurin series you found for f? 8. a) Find an equation for the tangent plane to the surface z = √√³ - 2y³ at the point (1,1,-1). b) Find the distance of the point (-1,1,0) from the plane you found in a). 9. Let a = 27+ 3 − k, b = 5ỉ – 3k, c = i − 2j+ k, be three vectors in the 3-dimensional space. a) Find the area of the parallelogram with sides the vectors a and 6. b) Find the volume of the parallelepiped with sides the vectors a, b, and c. c) Find the angle between the vectors a and b. (You may leave your answer as 0 = cos ¹().) b)
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