Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. k K = 0 3k + 1 . . . Select the correct answer below and fill in the answer box to complete your choice. O A. According to the Divergence Test, the series diverges because lim a = K -+ 0o (Simplify your answer.) O B. According to the Divergence Test, the series converges because lim a = K -+ 0o (Simplify your answer.) O C. The Divergence Test is inconclusive because lim ap = K-+ 0o (Simplify your answer.) O D. The Divergence Test is inconclusive because lim a does not exist. K -+ 0oUse the Integral Test to determine whether the following series converges after showing that the conditions of the Integral Test are satised. 00 2 k=0 2 dk+3 E> 2 1/x+3 Determine which conditions of the Integral Test are satised by the function f(x) = . Select all that apply. E] A. The function f(x) is negative for x 2 0. E] B. The function f(x) is an increasing function for x 2 0. [:1 C. The function f(x) is positive for x a 0. [:1 D. The function f(x) is a decreasing function for x a 0. [:1 E. The function f(x) has the property that ak = f(k) for k = O, 1, 2, 3... E] F. The function f(x) is continuous for x2 0. Use the Integral Test to determine whether the following series converges after showing that the conditions of the Integral Test are satised. 1 W 31/7k+3 E) 1 Determine which conditions of the Integral Test are satised by the function f(x) = . Select all that 31/7k + 3 apply. I] A. The function f(x) is positive for x 2 1. E] B. The function f(x) is a decreasing function for x 2 1. [:1 C. The function f(x) is continuous for x2 1. E] D. The function f(x) has the property that ak = f(k) for k =1, 2, 3, E] E. The function f(x) is an increasing function for x 2 1. [:1 F. The function f(x) is negative for x a 1. Use the Integral Test to determine whether the following series converges after showing that the conditions of the Integral Test are satised. 00 z ke -6k2 k=1 E> 2 Determine which conditions of the Integral Test are satised by the function f(x) = x e _ 6x . Select all that apply. E] A. The function f(x) is positive for x 2 1. E] B. The function f(x) is continuous for x2 1. E] C. The function f(x) is an increasing function for x 2 1. E] D. The function f(x) is a decreasing function for x 2 1. E] E. The function f(x) is negative for x 2 1. E] F. The function f(x) has the property that ak = f(k) for k = 1, 2, 3, Use the Integral Test to determine whether the following series converges after showing that the conditions of the Integral Test are satised. 1 Determine which conditions of the Integral Test are satised by the function f(x) = 2. Select all that x( In x) apply. E] A. The function f(x) is positive for x 2 4. E] B. The function f(x) has the property that ak = f(k) for k =1, 2, 3, E] c. The function f(x) is an increasing function for x 24. E] D. The function f(x) is negative for x 2 4. E] E. The function f(x) is a decreasing function for x 2 4. [:1 F. The function f(x) is continuous for x2 4. Use an appropriate test to determine whether the following series converges. 9 K = 1 . . . Select the correct choice below and fill in the answer box to complete your choice. O A. The series converges. It is a p-series with p = 9 O B. The series diverges by the Integral Test. The value of dx is 1 1X 5 9 O c. The series diverges by the Divergence Test. The value of lim is O D. The series diverges. It is a p-series with p = 9 O E. The series converges by the Divergence Test. The value of lim is