Evaluate the following. You must evaluate using a limit and not a definite integral. Clearly label answers for each section. Some formulas that might be helpful:   Simplify the following so that it does not use sigma notation: Now, find . If you have answered any part of this question, please select “True” below; otherwise, select “False.”

Perform the multiplication.

Write each expression in simplest form.

Question 9 (18 pts.)  For the following reaction, DRAW a full curved-arrow pushing mechanism for formation of the products and indicate the Lewis acid and base at each step (LA or LB) and whether they are also Bronsted acids and bases (BA or BB). Each step should have organic structures that are drawn in FULL LINE ANGLE STRUCTURES.     

When two rotating objects collide in a perfectly inelastic collision, which quantity is always conserved for an isolated system?

Exam 3 – Q11.pngThree solid spheres are attached to a light, rigid horizontal rod. The rod has a negligible mass. Sphere 1 has a mass of m1 ​= 0.40 kg, sphere 2 a mass of m2​ = 0.25 kg, and sphere 3 a mass of m3​ = 0.60 kg. The radius of each sphere is r = 0.030 m. The centers of the spheres are located along the x-axis, with sphere 1 at x = 0.00 m, sphere 2 at x = 0.30 m, and sphere 3 at x = 0.75 m. The system rotates about an axis through the center of sphere 3. Use I s p h e r e = 2 5 m r 2 . a. Determine the moment of inertia of sphere 1 about the axis. b. Determine the moment of inertia of sphere 2 about the axis. c. Determine the total moment of inertia of the system. d. If a torque of 0.15 Nm is applied, determine the angular acceleration.

The price index used to measure changes in the cost of living is the:

Decrease in capital per hour worked is shown in the figure above by the movement from B to _______. 

The three types of unemployment are:

What is the property described in part c called?