Weekly Tutorial 4 for Math. 69.107A,
Elementary Calculus I

Instructor: Dr. Angelo Mingarelli

Notes: These are group tutorials; each question is to be divided among the group (at most 5 students in a given group), solved and submitted to the T.A. at the end of the 50 min. period. NOTES ALLOWED, along with group interaction...All students within a group will be assigned the same grade for this tutorial...
This online test is meant to be printed and handed in.
Solutions will appear later on during the term ...

Group names (Please PRINT) & Student Numbers:

1. A veterinarian needs to anesthetize a 50 kg. dog with an anesthetic known as Sodium Pentobarbitol. It is known that a dog will be anesthetized when its bloodstream contains at least 45 x 10-6 grams of the anesthetic per kilogram of body weight. Assume that Sodium Pentobarbitol is eliminated exponentially from the dog's blood stream with a half-life of 5 hours. What single dose should the veterinarian administer to the dog in order to anesthetize it for one hour?

a) 2.585 x 10-3 g.
b) 3.657 x 10-1 g.
c) 2.585 x 10-1 g.
d) None of these

2. Calculate the derivative of the function y = Arcsin[sqrt(x)] at x = 1/2.

a) 0
b) -1
c) 1
d) None of these

3. Let f(x) = Arcsin[(x-b)/a] where a, b are constants and a > 0. What is the value of the derivative of f at x = b?

a) b
b) -1/a
c) 1/a
d) This value is undefined

4. Suppose that water is flowing down a pipe and we can measure the rate of flow at any time t. The table below gives readings (in liters/minute) taken at hourly intervals one afternoon.

Time = 1:00 2:00 3:00 4:00 5:00 6:00
Flow = 85 76 70 62 40 18

Estimate the total volume (in liters) of water that passed through the pipe between 1:00 p.m. and 6:00 p.m.

a) 333 liters
b) 200 liters
c) 158 liters
d) 415 liters

Check your answers in the adjoining box:

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