QUESTION 1

Given 1.1
fx) = x* -7x + 81 – 3

1.1.1 Determine the coordinates of the turning points of f(x).

1.1.2 Draw up a table of r and f(x), where x is ranging from x= -2 to 7.

1.1.3 Draw a neat graph of f(x) between these values and show the turning points on it.

1. 1.4 One root of the equation f(x) = x* – 7x* + 8x –

3 is close to 5

Use this value and one approximation of Taylor’s/Newton’s method
to determine a better approximation of this root

A thin sheet of ice is in the form of a circle. If the ice is melting in such a way
that the area of the sheet is decreasing at a rate of 0,5 m?/s at what rate is
the radius decreasing when the area of the sheet is 12 m2?

1.2 A cylindrical can with a bottom but no top with a volume of 30 cm must be
constructed.

Determine the dimensions of the can that will minimize the amount of material
needed to construct the can.

QUESTION 2

2.1 Determine Jy dx in each of the following cases:

2.1.1 sec TX

1+ tan TX (3)

2.1.2 y44 (3)

2.1.3
y 5+ 25X
2.1.4 cotA
2.1.5 =hn

2.2 Determine|ydr by resolving the integral into partial fractions:

QUESTION 3

3.1 Evaluate the definite integral:

3.2 Given:
y =X – 1 and y = (x- 1)
(2) 3.2.1 Calculate the coordinates of the points of intersection.
Make a neat sketch to show the enclosed area, the representative strip, and the point of intersection. (2)
3.2.2
(3) 3.2.3 Calculate the magnitude of the area in QUESTION 3.2.2.
Calculate the volume of the solid of revolution formed when the
area in QUESTION 3.2.2 is rotated about the x-axis. (4)
3.2.4
Calculate the second moment of area of a rectangular lamina with sides
8 cm X 4 cm and about a 4 cm side. (4)

QUESTION4
(4) 4.1 Determine the particular solution of x dy = y lny dx, given x = 2 when y = e.

4.2 Determine the general solution of =x – sin x.