Hello, I need help with question 31 30. A steel tank has the shape of a circular cylinder orientedvertically with diameter 4 m and height 5 m. The tankis currently filled to a level of 3 m with cooking oil thathas a density of 920 kg/m². Compute the work requiredto pump the oil out through a 1-m spout at the top of thetank.31. Find the average value of the function f(t) = sec² 1 on theinterval [0, 7/4].32. (a) Find the average value of the function f(x) = 1//xon the interval [1, 4].(b) Find the value e guaranteed by the Mean Value Theo-rem for Integrals such that fme = f(c).(c) Sketch the graph of ƒ on [1, 4] and a rectangle whosearea is the same as the area under the graph of f.33. If f is a continuous function, what is the limit as h → 0 ofthe average value of f on the interval [x, x + h]?34. Let Ri be the region bounded by y =x², y = 0, andx = b, where b > 0. Let Rz be the region bounded byy = x², x = 0, and y = b².(a) Is there a value of b such that R, and Rz have thesame area?(b) Is there a value of b such that R1 sweeps out the samevolume when rotated about the x-axis and the y-axis?(c) Is there a value of b such that R1 and Rz sweep outthe same volume when rotated about the x-axis?(d) Is there a value of b such that R1 and R2 sweep outthe same volume when rotated about the y-axis?

Name: Hello, I need help with question 31 30. A steel tank has the shape of
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Hello, I need help with question 31 30. A steel tank has the shape of a circular cylinder orientedvertically with diameter 4 m and height 5 m. The tankis currently filled to a level of 3 m with cooking oil thathas a density of 920 kg/m². Compute the