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    Assignment 1 Engineering Mathematics Ii: Instructions

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    ctjoa_1
    1. This document outlines the instructions for Assignment 1 in Engineering Mathematics II. It contains 5 questions testing skills in sequences, series, convergence tests, Taylor/Maclaurin series, and partial derivatives. 2. Students must submit their own original work through the online submission system by the due date. Plagiarism will result in disciplinary action and a grade of zero. 3. The assignment is worth 100% of the total grade and 15% of the student's final grade for the course. It covers topics from Units 1 and 2 of the class.

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    Assignment 1 Engineering Mathematics Ii: Instructions

    Uploaded by

    ctjoa_1
    26 views6 pages
    1. This document outlines the instructions for Assignment 1 in Engineering Mathematics II. It contains 5 questions testing skills in sequences, series, convergence tests, Taylor/Maclaurin series, and partial derivatives. 2. Students must submit their own original work through the online submission system by the due date. Plagiarism will result in disciplinary action and a grade of zero. 3. The assignment is worth 100% of the total grade and 15% of the student's final grade for the course. It covers topics from Units 1 and 2 of the class.

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    EM2

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    1. This document outlines the instructions for Assignment 1 in Engineering Mathematics II. It contains 5 questions testing skills in sequences, series, convergence tests, Taylor/Maclaurin series, and partial derivatives. 2. Students must submit their own original work through the online submission system by the due date. Plagiarism will result in disciplinary action and a grade of zero. 3. The assignment is worth 100% of the total grade and 15% of the student's final grade for the course. It covers topics from Units 1 and 2 of the class.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    26 views6 pages

    Assignment 1 Engineering Mathematics Ii: Instructions

    Uploaded by

    ctjoa_1
    1. This document outlines the instructions for Assignment 1 in Engineering Mathematics II. It contains 5 questions testing skills in sequences, series, convergence tests, Taylor/Maclaurin series, and partial derivatives. 2. Students must submit their own original work through the online submission system by the due date. Plagiarism will result in disciplinary action and a grade of zero. 3. The assignment is worth 100% of the total grade and 15% of the student's final grade for the course. It covers topics from Units 1 and 2 of the class.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    of 6

    Assignment 1

    ENGINEERING MATHEMATICS II

    Evidence of plagiarism or collusion will be taken seriously and the University


    regulations will be applied fully. You are advised to be familiar with the
    University’s definitions of plagiarism and collusion.

    Instructions:
    1. This is an individual assignment. No duplication of work will be tolerated.
    Any plagiarism or collusion may result in disciplinary action in addition to
    ZERO mark being awarded to all involved.

    2. You are to submit your answer through online submission system. You are
    not allowed to submit scanned handwritten works.

    3. Marks will be awarded for correct working steps and answer.

    4. The total marks for TMA 1 is 100 % and it contributes 15 % towards your
    total grade.

    5. TMA 1 covers topics from Unit 1 and Unit 2

    6. TMA 1 contains five (5) questions. Answer all questions in English .


    Question 1
    (a) List the first five terms of the following sequence

    ak  1   0.2 
    k
    (i)

    k 1
    (ii) ak 
    3k  1
    3  1
    k
    (iii) ak 
    k!
    (iv) ak 1  ak  5, a0  2
    ak 2  1
    (v) ak 1  , a0  3
    2ak  3
    (5 marks)
    (b) Find the general term ak of the sequence
    1 1 1 1 
    (i)  , , , ,...
     2 4 8 16 
    1 1 1 1 
    (ii)  , , , ,...
    2 4 6 8 
    (iii)  2, 7, 12, 17,...
     1 1 1 1 
    (iv) 1,  , ,  , ,...
     4 9 16 25 
     2 4 8 16 
    (v)   , ,  , ,...
     3 9 27 81 
    (5 marks)
    (c) Determine if the following sequences converges or diverges. If converges,
    find the limit

    ak  1   0.2 
    k
    (i)

    k3
    (ii) ak 
    k3  1
    3  5k 2
    (iii) ak 
    k  k2
      2k  1 ! 
    (iv) ak   
      2k  1 ! 
    3k  2
    (v) ak 1 
    5k
    (10 marks)

    Question 2
    (a) Find at least 8 partial summations of the following series. Determine if it is
    convergence or divergent. If it is convergent, find the sum.

    12
    (i) 
    n 1  5  n

    2n 2  1
    (ii)  n2  1
    n 1

     n 1

    (iii)   0.6 
    n 1
    (7.5 marks)
    (b) Determine whether the following series is convergent
    ( Hint: Geometric/Arithmetical/p-series)

    3 1 1
    (i) 1    
    4 2 4
    16 64
    (ii) 3  4   
    3 9

     3 
    n 1

    (iii) 
    n 1 4n

     n 
     3
    (iv)
    n 1


    1
    (v)  n 1
    4
    n
    (12.5 marks)
    Question 3
    (a) Use comparison test to determine the convergent of the following series

    1 1 1
    (i) 1  2
     3  4  ...
    2 3 4


    5
    (ii)  3n
    n 1
    2
     2n  1
    (5 marks)
    (b) Use D’Alembert’s ratio test to determine the convergent of the following
    series

    22 33 4 4
    (i) 1     ...
    2! 3! 4!

    1 2 3 4
    (ii)     ...
    2 3 4 5
    (5 marks)

    (c) Test the alternating series for convergence or divergence

     1
    n 1

    (i) 
    n 1 n


    3n  1
      1
    n
    (ii)
    n 1 2n  1
    (5 marks)

    (d) Determine whether the series is absolutely convergent or diverges by


    using ratio test.

     10 
    n

    (i) 
    n 1 n!
     2
    n
    (ii) 2
    n 1
    n

    (5 marks)
    Question 4
    (a) Find the radius of convergence and interval of convergence of the
    following series


    xn
    (i) n 1 n

      1
    n
    (ii) n 4n x n
    n 1

     1
    n 1
     xn
    (iii) n 1 n3
     x  2
    n

    (iv) n 1 n2  1
    (10 marks)
    (b) Find the Taylor series for f  x  centered at the given value of a.

    (i) f  x  1 x  x2, a  2
    (ii) f  x   x 3 , a  1
    (5 marks)
    (c) Find the Maclaurin series for f  x 

    (i) f  x   sin x
    f  x  1 x
    k
    (ii)

    (5 marks)

    Question 5
    Find the first partial derivatives of the following functions

    (a) f  x, y   2y  3 x y  xy
    5 6 2

    (b) f  x, y   3 x  5 y  9 x y  9 y  3 x  1
    2 2 2

    (c) f  x, y   4 xy sin x y
    2

    (d) f  x, y , z   e
    3 xyz

    (e) f  x, y , z   2z  x yz
    3 2

    (20 marks)

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