199957

3 C 22091
22. Let R be the region bounded by the graphs of x = — y? + 6y and x = 0. Find the volume of the
solid obtained by revolving R about the x-axis.

23. Find the area of the surface obtained by revolving the graph of x = y® on the interval [0, 1]
about y-axis.

(5 x 6 = 30 marks)
Section C
Answer any two questions.

Each question carries 10 marks.
24. (a) By translating the graph of y = x?, sketch the graphs of y = x? + 2 and y = (x — 2).
5 + & + +1 7 <0
(9) Let f(«)=42 if x =0
‏شر‎ +2۴ 1 ifx>0
Fina lim fx) and lim f(x). Does lim f(x)

x 07

exist. Justify your answer.

25. Sketch the graph of the function f(x) =2x° - 3 - 12: + 19.

3
26. Using the definition of the definite integral evaluate | (4-2).
=1

2
27. (a) Find the area of the region enclosed by the graphs of y = 810 + = 3
x +

(b) Find the volume of a right pyramid with a square base of side b and height h.
(2 x 10 = 20 marks)

199957