Group+C+Period+8

Welcome Group C Period 8. You are to complete 3, 9 and 15. Each member of the group is asked to contribute. Feel free to use the discussion forum to bounce ideas off one another.

3. a) π r^2h f('x)= π r^2

b) v= π r^2h f('x)= 2 πr c) v=(πr^2)(h) πhr^2h(dh/dy) + 2πrh(dr/dx)

9. a) A = lw da/dt = l(dw/dt) + w(dl/dt) da/dt = 24 - 10 da/dt = 14 cm^2/sec

b) P = 2l + 2w dp/dt = 2(dl/dt) + 2 (dw/dt) dp/dt = 2(-2) + 2(2) dp/dt = 0 cm/sec

c) L = (w^2 + l^2)^1/2 dl/dt = 1/2 (w^2+ l^2) (2w dw/dt + 2l dl/dt) 1/2 (169) ^-1/2 (20 - 48)

1/26 (-28) = -14/13 cm/sec = dl/dt

d) The area is increasing; its derivative is positive. The perimeter is unchanging; it's derivative is 0. The length of the diagonal is decreasing; its derivative is negative.

15. Cylinder: V=πr^2h (dv/dt)=π(2rh(dr/dt)+r^2) (dv/dt)=π(2(1.9)(6)(.001/3))+1.9^2 (dv/dt)=π(.0076)+3. 61 (dv/dt)=3.63

First take the derivative of the volume of a cylinder. However, since the height does not change as the cylinder expands outward, you do not need to take (dh/dt). after taking the derivative plug in the information given and solve.