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MATH 252: Calculus 2 m252t300a Test 3: Sequences, Series and Power Series 1 Page 1 of 4 0. Write your name in the upper right corner of this page. Write today’s date in the
upper left corner of this page. In Problem 1, find the exact value of the sum of the series. Show your calculations. A. !!!!
!!!!!!
In Problem 2, determine if the series is absolutely convergent (AC), conditionally convergent (CC) or divergent (D). A. !! !
!!!!!!!! B. !
!!!!!!!!
C. !! !
!!!!!!! D. !!
!!!!!!!!
E. !! ! !!!!!∗!"!""
!!!! F. !"#! !
!!!!!!!
MATH 252: Calculus 2 m252t300a Test 3: Sequences, Series and Power Series 1 Page 2 of 4 0. Write your name in the upper right corner of this page. Write today’s date in the
upper left corner of this page. In Problem 3, find the interval of convergence for the power series. A. !
!!!!!!! 𝑥 + 2 !
B. !! !
!!!!!!! 𝑥 + 2 !
C. !! !
!!! !!!!! 𝑥 + 2 !
In Problem 4, find the third degree Taylor polynomial approximating 𝑓 𝑥 near 𝑥 = 0. A. 𝑓 𝑥 = !
!!!
MATH 252: Calculus 2 m252t300a Test 3: Sequences, Series and Power Series 1 Page 3 of 4 0. Write your name in the upper right corner of this page. Write today’s date in the
upper left corner of this page. In Problem 5, suppose that 𝐺 4 = 10, 𝐺′ 4 = 5, 𝐺!! 4 = −8, and 𝐺!!!(4) = −24. A. Approximate 𝐺 3.9 . Show your calculations.
In Problem 6, find the sum of the series. Show your calculations. Round your answer to the nearest hundredth. A. !! !
!!!!!!!!
MATH 252: Calculus 2 m252t300a Test 3: Sequences, Series and Power Series 1 Page 4 of 4 0. Write your name in the upper right corner of this page. Write today’s date in the
upper left corner of this page. In Problem 7, suppose that the power series 𝐶! 𝑥 + 3 !!
!!! converges when 𝑥 = −8 and diverges when 𝑥 = −10. At each value of 𝑥, determine if the power series is absolutely convergent (AC), conditionally convergent (CC), divergent (D) or if the convergence of the power series cannot be determined (I). A. 𝑥 = 0
B. 𝑥 = 2
C. 𝑥 = 5
End of Test 3
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