MAT1581 ASSIGNMENT 3 2025 – STEP-BY-STEP CALCULATIONS PROVIDED (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.