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?

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Answered: 31. Find the average value of the…

Math

Calculus

31. Find the average value of the function f(1) = sec²t on the interval [0, 7/4].

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Hello, I need help with question 31

30. A steel tank has the shape of a circular cylinder oriented
vertically with diameter 4 m and height 5 m. The tank
is currently filled to a level of 3 m with cooking oil that
has a density of 920 kg/m². Compute the work required
to pump the oil out through a 1-m spout at the top of the
tank.
31. Find the average value of the function f(t) = sec² 1 on the
interval [0, 7/4].
32. (a) Find the average value of the function f(x) = 1//x
on 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 whose
area 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 of
the average value of f on the interval [x, x + h]?
34. Let Ri be the region bounded by y =x², y = 0, and
x = b, where b > 0. Let Rz be the region bounded by
y = x², x = 0, and y = b².
(a) Is there a value of b such that R, and Rz have the
same area?
(b) Is there a value of b such that R1 sweeps out the same
volume when rotated about the x-axis and the y-axis?
(c) Is there a value of b such that R1 and Rz sweep out
the same volume when rotated about the x-axis?
(d) Is there a value of b such that R1 and R2 sweep out
the same volume when rotated about the y-axis?

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