Math 20.3A section: ____________________
Student Name: ______________________________
ATENEO DE MANILA UNIVERSITY
MATHEMATICS DEPARTMENT
APPLIED CALCULUS FOR LIFE SCIENCES I (MATH 20.3A)
LECTURER: MR. ROBERT C. PANGILINAN
PRACTICE LONG EXAM # 3
February 12, 2011
Instructions:
Score: ___________
1. Time allotted for the exam is one (1) hour and twenty (20) minutes.
2. Only short bond papers are allowed to be used as answer sheets.
3. Show your complete solution on the answer sheets.
4. All final answers must be written in ink and boxed.
5. Scientific calculators are allowed.
6. Student’s name should be written in all pages of the answer sheet and on the questionnaire.
7. Answer sheets must be submitted together with this questionnaire on top.
8. DON’T FORGET TO SMILE AND PRAY
𝑑𝑦
of the equation 𝑦 5 + 𝑥 2 𝑦 3 = 1 + 𝑥 4 𝑦 and SIMPLIFY.
1.
Find
2.
Find the equation of the tangent line to the equation 𝑦 3 + 𝑥𝑦 − 𝑦 = 8𝑥 4 when x = 1.
3.
Assume x and y are functions of t, evaluate
4.
It is estimated that a person learning a certain assembly-line task takes
2+𝑥
𝑇(𝑥) =
2 + 𝑥2
𝑑𝑥
𝑑𝑦
𝑑𝑡
for 𝑥𝑒 𝑦 = 1 + 𝑙𝑛𝑥 𝑎𝑛𝑑
minutes to perform the task after x repetitions. Find
5.
Given 𝑓(𝑥) =
a.
b.
6.
𝑑𝑇
𝑑𝑡
if
𝑑𝑥
𝑑𝑡
[ 10 points]
𝑑𝑥
𝑑𝑡
= 6, 𝑥 = 1, 𝑦 = 0.
= 4 and 4 repetitions of the task have been performed.
[ 15 points]
[ 10 points]
[ 15 points]
𝑥2
2,
(𝑥−2)
find its local extrema if there are any and the intervals where the function is increasing and decreasing.
[ 10 points]
find its points of inflection if there are any and the intervals of the function where it is concave upward or downward [ 15 points]
The number of people P(t) (in hundreds) infected t days after an epidemic begins is approximated by
𝑃(𝑡) =
10𝑙𝑛(0.19𝑡+1)
0.19𝑡+1
When will the number of people infected start to decline?
7.
Letter
Grade: _______
[ 15 points]
A water tank has the shape of an inverted circular cone with base radius 2 m and height 4 m. If water is being pumped into the tank at a
rate of 23m3/min, find the rate at which the water level is rising when the water is 3 m deep.
[ 10 points]