c) Let f(x.y)= e. Find the directional derivative of f(xy) at the point (-3, 0) in the direction of the unit vector that makes an angle of with the positive x-axis. (6 marks) d) Find the maximum and minimum values of f(x.y)-2x - 2y subject to the constraint x² +y* =1. (6 marks) O Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![c)
Let f(x,y)= e"y, Find the directional derivative of f(x,y) at the point (-3, 0) in the
direction of the unit vector that makes an angle of with the positive x-axis.
(6 marks)
Find the maximum and minimum values of f(x, y)-2x - 2y subject to the constraint
d)
x + y? =1.
(6 marks)
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CS/FEB 2021/MAT495
QUESTION 3
The equation -0.5x + 2.5x+4.5 = 0 has a root that lies in the interval [5, 10]. Use
three iterations of the Bisection Method to estimate the root correct to four (4) decimal
places.
a)
(5 marks)
Use four iterations of the Newton's Method with X, = 3.5 to estimate the solution of the
equation x - 6x +11x-6.1= 0 correct to four (4) decimal places.
b)
(5 marks)
c)
Construct a finite difference table with three (3) difference columns for the data in Table
1. Then, use the Newton Forward Difference Interpolation Formula to estimate f(54).
Table 1
1
3
50
0.7071
55
0.7660
60
0.8192
65
f(x)
0.8660
(10 marks)
END OF QUESTION PAPER
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