Test #2 : Thursday 6/18 Topics: Length of a curve, surface area, Work, Fluid Force, Rectilinear motion.

Arclength: P 375 # 3 - 8, 13, 25 Don't forget: Must always check continuity and differentiability 1st. ( I will take off points if you don’t establish that the fcn is cont and diff and don’t just say it is, show me why. For ex: is cont and diff for all values of x because it is a polynomial function ( calc I theorem) or is cont for all x>0 and diff for all x>0, so it is cont and diff over [1,3].) If the arc length formula cannot be used b/c the function does not meet the differentiability requirement, you may be able to complete the problem by switching to the other formula ( dy instead of dx - see problem #8) Also remember we have a formula for the arclength of parametric equations ( must check cont and diff for both equations) (P 375 # 25)

Surface Area: P 380 # 1 - 8, 9,11,12, 23, 24 remember that SA is like Length – you have to check for cont/differentiability before applying the formula. Remember, with SA there is no choice: if revolved about the x – axis , use the dx formula; about the y-axis, dy For length and surface area problems, be careful with the algebra.

Work: 3 types of problems: 1) regular work problems - like the Rope/pulley problem or the rocket problem, 2) Springs, remember that when setting up the limits, that x represents the # of units stretched or compressed, so at natural length (equilibrium) we let x = 0. 3) Work involving removing liquid from a container

P 389, # 1,2, 6 – 9, 12, 14 – 19, 21 – 23, 25 Fluid force: P 405 # 3 - 8, 11,20, 21 (I will provide a copy of the table of densities on P 402)

Rectilinear motion: Know relationship between position, velocity and acceleration functions. Difference between distance and displacement, application problems involving motion along a straight line. (including vertical motion, which we will cover on Tuesday). P 329 # 5, 9, 15, 30 -33, 35HW for Vertical Motion: P 331 # 37 - 41