MATH 36 H Exercises
CHAPTER 5 Applications of the Derivative
1. Find the rate of change of the circumference of a circle with respect to the area, when area equals 4
square feet.
Ans. ft / sq. ft.
2. At what point of the parabola
2
y=x 3 x5 is the tangent
MATH 36 H
Axiomatic Development of the Real Number System
Exercises
I. Prove the following using mathematical induction.
1.
2.
for
and
3.
4.
is divisible by 4
5.
for
and
II. Find the first four elements of the sequence and determine whether it is converge
MATH 36 H
Guided Quiz
Applications of the Derivative
1. The base and base angles of an isosceles triangle are increasing at the respective rates of 2 feet
per second and 5 per second. When the base is 10 feet long and the base angles are 45, find the
rate
MATH 36-H 2nd Semester 2010-2011
Third Long Examination (Sample)
INSTRUCTIONS:
1. Write all answers legibly and according to the order as they appear in this questionnaire in your bluebook.
Avoid erasures.
2. ANY FORM OF CHEATING WILL BE SEVERELY PUNISHED
MATH 36-H 2nd Semester 2010-2011
Second Long Examination (Sample)
INSTRUCTIONS:
1. Write all answers legibly and according to the order as they appear in this questionnaire in
your bluebook. Avoid erasures.
2. ANY FORM OF CHEATING WILL BE SEVERELY PUNISHE
7.
2
y =8 x 4 p=8 p=2. The focus is at (2,0). Then the center of the circle is at (2, 0)
since the latus rectum of the parabola is a diameter.
2
2
2
2
Its radius is 4. The equation is ( x2) + y =16 x + y 4 x+ 416=0 .
2
8. Equation of the locus:
2
( x5) (