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Sma2214:Dicrete Mathematics Question Paper

Sma2214:Dicrete Mathematics

Course:Bachelor Of Business Information Technology

Institution: Meru University Of Science And Technology question papers

Exam Year:2013

QUESTION ONE (30 MARKS)
a) Evaluate
3 29 24+3
(3 Marks) b) Given that = 1 21 , show that the function is continuous at = 0. (3 Marks) c) Find the derivative, of = using first principles. (4 Marks) d) Find the derivative of = 32+5 3+4 . (3 Marks) e) Given a curve represented by the function 1 +1 + 1 +1 = (1,1) determine the equation of the tangent to the curve at = 1. (4 Marks) f) Find for the parametric equations = + , = 1 + (express your answer in terms of x only. (3 Marks) g) Show that (sin) = cot . (4 Marks) h) If 3 + 3 = 6,find (3 Marks) i) Evaluate 2 6 3 (2 Marks)
2
QUESTION TWO (20 MARKS)
a) Compute the limit lim1 54 1
(5 Marks) b) The function 3 + 3 2 = 5 represents a curve in the x-y plane. Determine the equation of the tangent line to the curve at = 1, = 2 and state the nature of point (1, 2). (5 Marks) c) i) Determine the turning points of the curve = 23 + 32 36 + 10. (4 Marks) ii) For each point in (i) above, state whether it is a local minimum, local maximum or neither, on the graph. (3 Marks) d) Given = 42 , determine the approximate change in y if x changes from 1 to 1.02. (3 Marks)
QUESTION THREE (20 MARKS)
a) differentiate = 3 tan2 (4 Marks) b) given that = 2sin = cos2, find 2 2 (4 Marks) c) find from the first principles given that = sin. (4 Marks) d) find for the following equations; i. = (4 2)2 (2 3) (4 Marks) ii. = tan1 (4 Marks)
QUESTION FOUR (20 MARKS)
a) Show that
log = 1
(4 Marks)
b) If = 1 2++1 4 , determine . (4 Marks) c) The distance y metres moved by an object in a straight line in time t seconds is given by: = 3 62 + 9 1 . Determine its velocity and acceleration when; i. = 0 ii. = 1.5 (6 Marks) d) Find the values of C and D for which the following function is continuous;
=
2, < 1 2 + , 1 < 2 4, 2 (6 Marks)

Sma2214:Dicrete Mathematics Question Paper

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