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Sma2102:Calculus 2 Question Paper

Sma2102:Calculus 2

Course:Bachelor Of Science In Computer Science

Institution: Dedan Kimathi University Of Technology question papers

Exam Year:2012

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DEDAN KIMATHI UNIVERSITY OF TECHNOLOGY
UNIVERSITY EXAMINATIONS 2011/2012
YEAR TWO SEMESTER I EXAMINATION FOR DEGREE OF
BACHELOR OF SCIENCE IN COMPUTER SCIENCE
SMA2102
CALCULUS 2
Question ONE ( 30 Marks)
a) If x= and y=2at, find (4mks)
b) Evaluate (x+1)+1) (4mks)
c) Express in the form a+bj (8mks)
d) Resolve into partial fractions (5mks)
e) Evaluate (5mks)
f) An object moving in a straight line has its velocity v ms-1 and any time t-sec given by where x m is the displacement at time t sec. Find where the object is when the acceleration is 30 ms-2 (4mks)
g) Find the length of the arc of the graph of y=x3/2 between (1,1) and (4,8) (5mks)
Question TWO (20 marks)
a) Evaluate (8mks)
b) Integrate (5mks)
c) Evaluate (7mks)
Question THREE (20 marks)
a) Use the trapezoidal rule to evaluate using 6 intervals. Give the answer correct to 4 significant figures. (10mks)
b) Determine the area enclosed by the 2 curves y= and . If this area is rotated 360 degrees, about the x-axis. Determine the volume of the solid of revolution produced. (10mks)
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Question FOUR (20 marks)
a) Using Demoivre’s theorem, prove that cos4?= (7mks)
b) Given that Z= express Z in the form (5mks)
c) Find the cube root of 2+2j (8mks)
Question FIVE (20 marks)
a) The time of swing t of a pendulum is given by T=KvL, where k is ia constant. Determine the percentage change in the time of swing, if the length of the swing changes from 32.1cm to 32.0cm. (8mks)
b) If determine the values f p and q (6mks)
c) Find the equations of the tangent to the curve y=, at the point (1,-2) (6mks)

Sma2102:Calculus 2 Question Paper

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