Midterm 2 / 2012.12.4 / Calculus for the Biosciences / MAT 1193.006
Name:
Please show all work. Supply brief narration with your solutions and draw conclusions.
1. Find y 0 where
(a) y =
cos(5x)
x2
(b) y = xx
2
(c) cos(3y) + exp(2y) = x2
2. You have 20 meters of fence and want to build a rectangular enclosure for your lab
animals against an existing wall, which will form one side of the enclosure. What should
the dimensions of the enclosure be to maximize the enclosed area? What is that area?
3. Evaluate the following limits using l’Hôpital’s rule. Specify which case you are using.
ex − 1
(a) lim
x→0 sin x
2
(b) lim x ln x
x→0+
(c) lim
x→0+
1
1
−√
x
x
4. Find antiderivatives for the following functions
(a)
1
1 + 9x2
(b) x cos(2x2 )
(c) x2 cos(2x)
5. After an initial bolus injection of 15 mg of a drug, a patient is placed on a drip delivering
1.2 mg per hour. If the drug is cleared by the patient at a rate of 0.8 − 0.1t2 mg/h as a
function of time, what is the amount of drug in the patient 6 hours later?
1
2
3
4
5
total (50)
Prelim. course grade:
%
%
THE UNIVERSITY OF TEXAS AT SAN ANTONIO