MTH603 Assignment 1 Solution and Discussion
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Re: MTH603 Assignment 1 Solution and Discussion
Assignment No. 1 MTH603 (Spring 2022)
Total Marks: 20
Due Date: 8th June, 2022DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
• To solve this assignment, you should have good command over 1-8 lectures.
• Upload assignments properly through the LMS, No Assignment will be accepted through email.
• Write your ID on the top of your solution file.
Don’t use colored backgrounds in your solution files.
Use Math Type or Equation Editor, etc. for mathematical symbols.
You should remember that if the solution files of some students are finding the same (copied), we will reward zero marks to all those students.
Make a solution by yourself and protect your work from other students, otherwise both original and copied assignments will be awarded zero marks.
Also remember that you are supposed to submit your assignment in Word format, any other format like scanned images, etc. will not be accepted and be awarded zero marksQuestion 1
Find a real root of the equation 2x+cos(x)+e^x=0
using Bisection Method
using Newton Raphson Method
Also compare the results and comment which of the methods performs better and which is worst.
You will consider x_0=-0.6557 as a best approximation while comparing the roots.Note:
In each of the above methods,you are required to perform three iterations. -
C cyberian marked this topic as a question on
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Re: MTH603 Assignment 1 Solution and Discussion
Assignment No. 1 MTH603 (Spring 2022)
Total Marks: 20
Due Date: 8th June, 2022DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
• To solve this assignment, you should have good command over 1-8 lectures.
• Upload assignments properly through the LMS, No Assignment will be accepted through email.
• Write your ID on the top of your solution file.
Don’t use colored backgrounds in your solution files.
Use Math Type or Equation Editor, etc. for mathematical symbols.
You should remember that if the solution files of some students are finding the same (copied), we will reward zero marks to all those students.
Make a solution by yourself and protect your work from other students, otherwise both original and copied assignments will be awarded zero marks.
Also remember that you are supposed to submit your assignment in Word format, any other format like scanned images, etc. will not be accepted and be awarded zero marksQuestion 1
Find a real root of the equation 2x+cos(x)+e^x=0
using Bisection Method
using Newton Raphson Method
Also compare the results and comment which of the methods performs better and which is worst.
You will consider x_0=-0.6557 as a best approximation while comparing the roots.Note:
In each of the above methods,you are required to perform three iterations.@cyberian said in MTH603 Assignment 1 Solution and Discussion:
Find a real root of the equation 2x+cos(x)+e^x=0
using Bisection Method


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Re: MTH603 Assignment 1 Solution and Discussion
Assignment No. 1 MTH603 (Spring 2022)
Total Marks: 20
Due Date: 8th June, 2022DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
• To solve this assignment, you should have good command over 1-8 lectures.
• Upload assignments properly through the LMS, No Assignment will be accepted through email.
• Write your ID on the top of your solution file.
Don’t use colored backgrounds in your solution files.
Use Math Type or Equation Editor, etc. for mathematical symbols.
You should remember that if the solution files of some students are finding the same (copied), we will reward zero marks to all those students.
Make a solution by yourself and protect your work from other students, otherwise both original and copied assignments will be awarded zero marks.
Also remember that you are supposed to submit your assignment in Word format, any other format like scanned images, etc. will not be accepted and be awarded zero marksQuestion 1
Find a real root of the equation 2x+cos(x)+e^x=0
using Bisection Method
using Newton Raphson Method
Also compare the results and comment which of the methods performs better and which is worst.
You will consider x_0=-0.6557 as a best approximation while comparing the roots.Note:
In each of the above methods,you are required to perform three iterations. -
C cyberian has marked this topic as solved on
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Only students of Section: Nabeela Wali shall solve this Assignment.
Assignment # 01 MTH603 (Spring 2024)
Marks: 10
Due Date: May 6, 2024
DON’T MISS THESE: Important instructions before attempting the solution and submission of this assignment:
⚫ Lectures 3-10 are encompassed in Assignment 1.
⚫ Only students in Section: Nabeela Wali shall complete this Assignment.
⚫ Students in other teacher’s section will be completing a different assignment and are strictly prohibited from solving this one.
⚫ Submitting a copied assignment or irrelevant assignment will result in a zero grade.
⚫ Assignment 1 is due on May 6, 2024.
⚫ Properly Upload the solution of this assignment in MS Word format on LMS as per the previous practice.
Question 1 5 Marks
Find a root of the equation 𝑥3 − 3𝑥 − 5 = 0, in the interval (2,3) using Bisection Method after three Iterations.
Note: Accuracy up to four decimal places is required.
Question 2 5 Marks
Find a root of the following equation in the interval (0,1) using Newton-Raphson Method after three iterations
𝑥𝑒𝑥 − cos 𝑥 = 0
Take Initial value 0.5.
Note: Accuracy up to four decimal places is required. Here is a transcendental equation all the calculation should be done in the radians mode. -
Only students of Section: Nabeela Wali shall solve this Assignment.
Assignment # 01 MTH603 (Spring 2024)
Marks: 10
Due Date: May 6, 2024
DON’T MISS THESE: Important instructions before attempting the solution and submission of this assignment:
⚫ Lectures 3-10 are encompassed in Assignment 1.
⚫ Only students in Section: Nabeela Wali shall complete this Assignment.
⚫ Students in other teacher’s section will be completing a different assignment and are strictly prohibited from solving this one.
⚫ Submitting a copied assignment or irrelevant assignment will result in a zero grade.
⚫ Assignment 1 is due on May 6, 2024.
⚫ Properly Upload the solution of this assignment in MS Word format on LMS as per the previous practice.
Question 1 5 Marks
Find a root of the equation 𝑥3 − 3𝑥 − 5 = 0, in the interval (2,3) using Bisection Method after three Iterations.
Note: Accuracy up to four decimal places is required.
Question 2 5 Marks
Find a root of the following equation in the interval (0,1) using Newton-Raphson Method after three iterations
𝑥𝑒𝑥 − cos 𝑥 = 0
Take Initial value 0.5.
Note: Accuracy up to four decimal places is required. Here is a transcendental equation all the calculation should be done in the radians mode.@cyberian said in MTH603 Assignment 1 Solution and Discussion:
Question 1 5 Marks
Find a root of the equation 𝑥3 − 3𝑥 − 5 = 0, in the interval (2,3) using Bisection Method after three Iterations.
Note: Accuracy up to four decimal places is required.

MTH603 - Assignment 1 - Spring 2024 - Nabeela Wali - Solution file.pdf
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Assignment # 01 MTH603 (Summer 2024)
Marks: 10
Due Date: 21.09 2024
DON’T MISS THESE: Important instructions before attempting the solution and
submission of this assignment:
Lectures 23-30 are encompassed in Assignment 1.
Assignment 1 is due on 21 September 2024.
Properly Upload the solution of this assignment in MS Word format on
LMS as per the previous practice.
Question 1 [Marks 5]
First construct the divided difference table and then find the interpolating
polynomial of the following function 𝑦 = 𝑓(𝑥) by Newton’s Divided Difference
Formula.
𝑥 0 𝜋
𝜋
2
𝑦 = 𝑓(𝑥) 0 1 0
Question 2 [Marks 5]
Compute 𝑓′(1.5), from the following tabular data using the forward difference
formula for derivative.
𝑥 1.5 2.0 2.5 3.0 3.5 4.0
𝑓(𝑥) 3.375 7.000 13.625 24.000 38.875 59.000 -
Assignment # 01 MTH603 (Summer 2024)
Marks: 10
Due Date: 21.09 2024
DON’T MISS THESE: Important instructions before attempting the solution and
submission of this assignment:
Lectures 23-30 are encompassed in Assignment 1.
Assignment 1 is due on 21 September 2024.
Properly Upload the solution of this assignment in MS Word format on
LMS as per the previous practice.
Question 1 [Marks 5]
First construct the divided difference table and then find the interpolating
polynomial of the following function 𝑦 = 𝑓(𝑥) by Newton’s Divided Difference
Formula.
𝑥 0 𝜋
𝜋
2
𝑦 = 𝑓(𝑥) 0 1 0
Question 2 [Marks 5]
Compute 𝑓′(1.5), from the following tabular data using the forward difference
formula for derivative.
𝑥 1.5 2.0 2.5 3.0 3.5 4.0
𝑓(𝑥) 3.375 7.000 13.625 24.000 38.875 59.000@zaasmi said in MTH603 Assignment 1 Solution and Discussion:
Assignment # 01 MTH603 (Summer 2024)
Marks: 10
Due Date: 21.09 2024
DON’T MISS THESE: Important instructions before attempting the solution and
submission of this assignment:
Lectures 23-30 are encompassed in Assignment 1.
Assignment 1 is due on 21 September 2024.
Properly Upload the solution of this assignment in MS Word format on
LMS as per the previous practice.
Question 1 [Marks 5]
First construct the divided difference table and then find the interpolating
polynomial of the following function 𝑦 = 𝑓(𝑥) by Newton’s Divided Difference
Formula.
𝑥 0 𝜋
𝜋
2
𝑦 = 𝑓(𝑥) 0 1 0
Question 2 [Marks 5]
Compute 𝑓′(1.5), from the following tabular data using the forward difference
formula for derivative.
𝑥 1.5 2.0 2.5 3.0 3.5 4.0
𝑓(𝑥) 3.375 7.000 13.625 24.000 38.875 59.000 -
@zaasmi said in MTH603 Assignment 1 Solution and Discussion:
Assignment # 01 MTH603 (Summer 2024)
Marks: 10
Due Date: 21.09 2024
DON’T MISS THESE: Important instructions before attempting the solution and
submission of this assignment:
Lectures 23-30 are encompassed in Assignment 1.
Assignment 1 is due on 21 September 2024.
Properly Upload the solution of this assignment in MS Word format on
LMS as per the previous practice.
Question 1 [Marks 5]
First construct the divided difference table and then find the interpolating
polynomial of the following function 𝑦 = 𝑓(𝑥) by Newton’s Divided Difference
Formula.
𝑥 0 𝜋
𝜋
2
𝑦 = 𝑓(𝑥) 0 1 0
Question 2 [Marks 5]
Compute 𝑓′(1.5), from the following tabular data using the forward difference
formula for derivative.
𝑥 1.5 2.0 2.5 3.0 3.5 4.0
𝑓(𝑥) 3.375 7.000 13.625 24.000 38.875 59.000@cyberian said in MTH603 Assignment 1 Solution and Discussion:
@zaasmi said in MTH603 Assignment 1 Solution and Discussion:
Assignment # 01 MTH603 (Summer 2024)
Marks: 10
Due Date: 21.09 2024
DON’T MISS THESE: Important instructions before attempting the solution and
submission of this assignment:
Lectures 23-30 are encompassed in Assignment 1.
Assignment 1 is due on 21 September 2024.
Properly Upload the solution of this assignment in MS Word format on
LMS as per the previous practice.
Question 1 [Marks 5]
First construct the divided difference table and then find the interpolating
polynomial of the following function 𝑦 = 𝑓(𝑥) by Newton’s Divided Difference
Formula.
𝑥 0 𝜋
𝜋
2
𝑦 = 𝑓(𝑥) 0 1 0
Question 2 [Marks 5]
Compute 𝑓′(1.5), from the following tabular data using the forward difference
formula for derivative.
𝑥 1.5 2.0 2.5 3.0 3.5 4.0
𝑓(𝑥) 3.375 7.000 13.625 24.000 38.875 59.000



