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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.
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. Submit your assignment to the Online Assignment Submission (OAS) system. Submission of assignments in hard copy will not be accepted.
3. The total marks for assignment 1 are 100 Marks and contributes 25% towards the total grade. Marks will be awarded for correct working steps and answer.
4. Assignment 1 covers topics from Unit 1 and Unit 2.
5. Your assignment must be word processed in Time New Roman or Cambria Math 12pt font. Any additional appendices or attachments must be placed at the end of the submitted document. Handwritten assignments and photo snap shot will not be accepted.
6. Students are required to attach the Assignment Declaration Form as the front cover of their assignments. No duplication of work will be tolerated. Any plagiarism or collusion may result in disciplinary action to all parties involved.
a) A technology company issues shares at an initial price of RM25. The stock price increases by 15% each year
i. Show that the stock price follows a geometric sequence. [3 Marks]
ii. Calculate the stock price eight years after issue. [2 Marks]
b) In an electrical circuit, resistors are connected in series. The first resistor has a resistance of 12 Ω. Each subsequent resistor’s resistance increases by a fixed amount from the previous one, and the total resistance of the first 4 resistors is 66 .
i. Find the common difference of this arithmetic sequence of resistances. [5 Marks]
ii. Show that the total resistance of the first n resistors is given by:
𝑛 𝑆𝑛 = 2 (3𝑛+21) [5 Marks]
iii. Find how many resistors are needed for the total resistance to exceed 300Ω [10 Marks]
a) Determine the limit of the following sequences.
3 ∞
i. { 1 / (2n⁴ + 3) }, n = 1 → ∞ [5 Marks]
ii. { (3n⁴ + 2n² − 5) / (5 + 4n³ + 7) }, n = 1 → ∞ [5 Marks]
iii. { (5n⁴ − 2n + 2) / (2n⁴ + n² + 7) }, n = 1 → ∞ [5 Marks]
b) Determine whether the following series is convergent,
conditionally convergent or divergent.
i. ∑n=1∞ (-1)n+1 − n³ [3 Marks]
ii. ∑n=1∞ n ______ ncos² − nπ² [7 Marks]
Consider the integral ∫0.21 x³ dx
i. Compute the exact value of the integral. [3 Marks]
ii. Compute the Trapezoidal rule approximation with 𝑛 =4 subintervals. [10 Marks]
iii. Compute Simpson’s rule approximation with 𝑛 =4 subintervals. [10 Marks]
iv. Justify whether each approximation is an overestimate or underestimate. [2 Marks]
Provide your answers in 4 decimal places.
Find the root of an equation 𝑓(𝑥)=𝑥3 −𝑥−1 using Bisection method. Given the interval [1,2]. Perform six (6) iterations. Write your answers to 4 decimal places.
[25 Marks]
End Of Assignment 1 Questions
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