MAT1581
Assignment 03
Due 5 August 2025
, Student Name: MAT1581 Assignment 03
MAT1581 Assignment 03
Due Date: Tuesday, 5 August 2025
Instructions
• Show all your working clearly.
• Simplify final answers where applicable.
• Answers must be written in terms of factorials, nCr, or nP r where specified.
• Do not use a calculator.
Question 1: Limits (6 Marks)
Problem 1.1
Determine:
x3 − 2
lim
x→−1 x4 + 4x − 3
Step 1: Substitute x = −1
x3 − 2 = (−1)3 − 2 = −1 − 2 = −3
x4 + 4x − 3 = (−1)4 + 4(−1) − 3 = 1 − 4 − 3 = −6
Step 2: Evaluate since denominator is non-zero
x3 − 2 −3 1
lim 4
= =
x→−1 x + 4x − 3 −6 2
Final Answer:
x3 − 2 1
lim
4
=
x→−1 x + 4x − 3 2
Page 1
Assignment 03
Due 5 August 2025
, Student Name: MAT1581 Assignment 03
MAT1581 Assignment 03
Due Date: Tuesday, 5 August 2025
Instructions
• Show all your working clearly.
• Simplify final answers where applicable.
• Answers must be written in terms of factorials, nCr, or nP r where specified.
• Do not use a calculator.
Question 1: Limits (6 Marks)
Problem 1.1
Determine:
x3 − 2
lim
x→−1 x4 + 4x − 3
Step 1: Substitute x = −1
x3 − 2 = (−1)3 − 2 = −1 − 2 = −3
x4 + 4x − 3 = (−1)4 + 4(−1) − 3 = 1 − 4 − 3 = −6
Step 2: Evaluate since denominator is non-zero
x3 − 2 −3 1
lim 4
= =
x→−1 x + 4x − 3 −6 2
Final Answer:
x3 − 2 1
lim
4
=
x→−1 x + 4x − 3 2
Page 1
