Author: Anonymous

Suppose that we are asked to find the area (A) between the curves    and   on the interval . What are the intersection points of these two curves on the interval? There are four possible points listed. If you do not need all of them enter “none” (without quotes) in the last boxes you do not need below. Make sure you enter the intersection points from smallest to largest. [intpt1] [intpt2] [intpt3] [intpt4] Hints:  The following identity holds for all x:   To enter the substitution , you should type “3 (x+1)^2 + atan(pi x)” (without the quotes).

Suppose that we are asked to evaluate the following indefinite integral: .   If we set and , then what is an expression for I as a function of only u and v (NOT x)?  Hints: Recall the list of trig identities you memorized and try to apply more than one of them if you need to use more than one.  We have the following identity for all real x: .

A continuous-time Markov chain has state space S ={0,1,2,} and the following generator matrix 

To handle Type B jobs, processor 3 is purchased. Then type B arrivals are sent to processor 3 with probability 0.4 (and to processor 2 with probability 0.6). What is the expected interarrival time in minutes between Type B arrivals to processor 3? 

What device did Dr Greenberg (and others) mention that is used to measure density (or stiffness) of a material?

Which of the following is TRUE regarding cervical orthoses:

Based upon the Physical Stress Theory (PST), what are the two primary questions to ask in evaluation and treatment? (1 point each for a total of 2 points)

What is the probability that there will be zero arrival of type B job between 1PM and 1:30PM? (answer up to 4 decimals e.g. x.xxxx)

Predict the direction of the reaction below based on pKa values

Mr. Rodriguez is your patient who lives with his wife and adult son in a single story house with no steps to enter. He is a 63 year old man who recently had a stroke resulting in some motor deficits of his left lower extremity. He is cognitively intact and has some extensor tone in his left ankle. He has hypertension that is now being controlled with medication. He has no other significant medical issues at this time. When you observe Mr. Rodriguez ambulate, he uses a large based quad cane and requires min assist for balance during left stance due to some instability and his left knee hyperextending. His bilateral upper extremity and right lower extremity strength and ROM are noted to be WFL. His left lower extremity strength is grossly 4-/5 at the hip and knee,  and 1/5 for both DF and PF. PROM is WFL throughout the left lower extremity.  1) Name two possible orthoses you would consider using to improve this patient’s functional mobility (1/2 point each for a total of 1 point)):1a)1b) 2) Of the two orthoses you mentioned above (1a and 1b), which one do you think would be the best choice for Mr. Rodriguez and why? (2 points)