MAT1581 Assignment 3 Memo | Due 5 August 2025

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MAT1581 Assignment 3 Memo | Due 5 August 2025. Step by Step Calculations Provided. 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
Question 2: 22 Marks
Differentiate the following to the appropriate independent variable and simplify where possible:
(2.1) y = (4)
1
x
−
√
cos x
(2.2) y = (x3 + 2)(x2 − 2x + 1) (6)
(2.3) y = (6)
√
1 + tan2 x
sec2 x
(2.4) y = ln ex (6)

x − 2
x + 3
34
Question 3: 4 Marks
The loading distribution y on a beam is given by y = −25×2 + 45x.
Question 4: 9 Marks
Given the curve y = 2×3 + 3×2 − 12x. Find the turning points and the intercepts with the axes. Sketch the
curve.