For the following indefinite integral, find the full power series centered at x = 0 and then give the first 5 nonzero terms of the power series and the open interval of convergence.

Simplify (1/2)4th power a. (1/16) b.(1/8) c.(1/4)

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?

Acommunity group is building a garden on a rectangular lot of land. the lot measures 5x by 10x and the garden will be circular with a radius of 3x. how much of the land will be left over after the garden is built? a. 41 pi x^2 b. x^2 (50 - 9 pi) c. x^2 (50 - 3 pi) d. 41x^2