, MAT1581 Assignment 3 (COMPLETE ANSWERS)
Semester 2 2025 - DUE 5 August 2025; 100%
TRUSTED Complete, trusted solutions and
explanations.
Question 1: 6 Marks Determine the following limits: (1.1) lim (3)
x→−1 x3 − 2 x4 + 4x − 3 (1.2) lim (3) x→3 x3 − 8 x2 − 4
Step 1: Evaluate numerator and denominator directly
Numerator:
x3−2=(−1)3−2=−1−2=−3
x^3 - 2 = (-1)^3 - 2 = -1 - 2 = -3
Denominator:
x4+4x−3=(−1)4+4(−1)−3=1−4−3=−6
x^4 + 4x - 3 =(-1)^4 + 4(-1) - 3 = 1 - 4 - 3
= -6x4+4x−3=(−1)4+4(−1)−3=1−4−3=−6
Step 2: Plug in values
=
✅ Final Answer (1.1):
Semester 2 2025 - DUE 5 August 2025; 100%
TRUSTED Complete, trusted solutions and
explanations.
Question 1: 6 Marks Determine the following limits: (1.1) lim (3)
x→−1 x3 − 2 x4 + 4x − 3 (1.2) lim (3) x→3 x3 − 8 x2 − 4
Step 1: Evaluate numerator and denominator directly
Numerator:
x3−2=(−1)3−2=−1−2=−3
x^3 - 2 = (-1)^3 - 2 = -1 - 2 = -3
Denominator:
x4+4x−3=(−1)4+4(−1)−3=1−4−3=−6
x^4 + 4x - 3 =(-1)^4 + 4(-1) - 3 = 1 - 4 - 3
= -6x4+4x−3=(−1)4+4(−1)−3=1−4−3=−6
Step 2: Plug in values
=
✅ Final Answer (1.1):
