MAT1581 Assignment 3 Semester 2 2023.

MAT1581 Assignment
3 Semester 2, 2023.

, MAT1581 Assignment 3 Semester 2, 2023
This assignment is a written assignment based on Study Guide 2, Chapter 6 and contributes 25% to your year
mark. You must work through the Chapter completely before you start answering the questions.
Pay attention to how you write down your answers. Your reasoning must be clear to the marker.
Give answers to two decimal places where applicable and angles in radians where applicable.
Show steps in answers.


QUESTION 1
Determine the following limits:
x 2  3x  4
1.1 lim (2)
x0 x3  2
n x
1.2 lim (3)
x 1 x2 1
[5]
QUESTION 2
dy
Determine of the following and simplify if possible:
dx
2.1 y  x cos5 x (2)

2.2 y  4 x  x2 (3)

2.3 
y  n sin e 3 x  (3)

[8]

QUESTION 3
2x
Determine the gradient of the curve y  2
at the point  2, 4  [5]
x 5
QUESTION 4
A particle has a displacement s, given by s  30t  27t 2  3t 3 meters, where t is in seconds.

Determine the time at which the acceleration will be zero. [3]
Total: 21




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