Assignment 1
Semester I Session 1435/1436 AHStudent Name :
Student ID :
Course Code : COCS 324
Total Marks
Course Name : Advanced Mathematics for Computing Date To Students : Tuesday, November 11, 2014
Date To Submit : By latest Thursday, November 20, 2014
5
Number of Exam Pages : 05
Declaration of Student: Marks
Outcome A /02 Marks
I declare that the answers given below are of my own work. I fully understand any answers provided which
are shared and discussed by colleagues.
Outcome B /02 Marks
Outcome J /01 Marks
Student Signature:
Total Marks
(In Figure) /05 Marks
Total Marks
(In Words) Instructions to Candidates:
There are three outcomes(A, Band J) in this paper. Read each question carefully. Figure in the right hand side shows marks.
Answer each question according to the instruction provided. Give figure whenever necessary. Give code whenever necessary.
Outcome A
Q.1a Find the derivative of the following function
i)
ii) iii) iv) v)
Answer:
Q.1b Find the derivative of the following function using product rule i)
ii) iii)
Answer
Q.1c Find the derivative of the following function using quotient rules
i) ii) iii)
iv)
Answer
Q2.a
i)
Find the tangent line to at .ii)
Determine where, if anywhere, the tangent line to is parallel to the line .iii)
Find the equation of the tangent line to at .
Answer:
Q.2b
The position of an object at any time t is given by . (a) Determine the velocity of the object at any time t.
(b) Does the object ever stop changing?
(c) When is the object moving to the right and when is the object moving to the left?
Answer
Q.2c
i) For a certain rectangle the length of one side is always three times the length of the other side.
(a) If the shorter side is decreasing at a rate of 2 inches/minute at what rate is the longer side decreasing?
(b) At what rate is the enclosed area decreasing when the shorter side is 6 inches long and is decreasing at a rate of 2 inches/minute?
ii) A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0.5 m2/sec at what rate is the radius decreasing when the area of the sheet is 12 m2 ?
Answer
Outcome B
Q.3a Evaluate each of the following indefinite integrals.
i)
ii)
iii) Answer
Q.3b
Evaluate each of the following integrals, if possible. If it is not possible clearly explain why it is not possible to evaluate the integral.
i) ii) iii)
iv)
Answer:
Q.3c
Evaluate each of the following integrals.
i)
ii) iii) iv) Answer:
Outcome J
Q. 4a
i) A plane is 750 meters in the air flying parallel to the ground at a speed of 100 m/s and is initially 2.5 kilometers away from a radar station. At what rate is the distance between the plane and the radar station changing (a) initially and (b) 30 seconds after it passes over the radar station? See the sketch below to help visualize the problem.
ii) Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of 2 ft/sec and the other person starts going up in the elevator at a rate of 7 ft/sec. What rate is the distance between the two people changing 15 seconds later?
Answer:
Q.4b
i) D
etermine the area below and above the x-axis ii) Determine the area to the left of and to the right of .iii) Determine the area of the region bounded by the given set of curves.
a. , , between ween and
b. , , between and
c. , , between and
Answer
