Calculus 2 :

Section 8.2: Problem 1 (1 point) Consider the series 4/10 + 16/100 - 64/1000 + 256/10000 + . . . Determine whether the series converges, and if it converges, determine its value. Enter the value if the series converges, or enter DIE if it diverges:Section 8.2: Problem 10 1 point) Find the values of x so that the series below converges. (x - 10) Give your answer in interval notation. CSection 8.2: Problem 4 (1 point) Given: 5n An = 2n + 7 For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, -INF if it diverges to minus infinity, or DIV otherwise. (a) The series (An.). n=1 (b) The sequence {An}.\fSection 8.2: Problem 9 (1 point) Find the values of x so that the series below converges. E n=1 Give your answer in interval notation.Section 7 6: Problem 3 [1 point) Suppose that 2 J of work are needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. How much work (in J} is needed to stetd'u it from 35 cm to 4|] cm? Work done = E] J Section 7 6: Problem 5 (1 point) An aquarium 2 m long, 1m wide, and 1 m deep is full of water. Find the work (in J) needed to pump half of the water out of the aquarium. Use the fact that the density of water is 1000 kg/m3. Work done =Section 7 6: Problem 6 (1 point) A circular swimming pool has a diameter of 14 m. The circular side of the pool is 4 m high, and the depth of the water is 2.5 m. (The acceleration due to gravity is 9.8 m/s' and the density of water is 1000 kg/m3.) How much work (in Joules) is required to: (a) pump all of the water over the side? (b) pump all of the water out of an outlet 1 m over the side