Sma2113:Maths For Science Question Paper
Sma2113:Maths For Science
Course:Bachelor Of Computer Science
Institution: Meru University Of Science And Technology question papers
Exam Year:2012
QUESTION ONE (30 MARKS)
a) Evaluate
???3 ?????? ??2-9 ??2-4??+3
(3 Marks) b) Given that ?? ?? = 1 ??2-1 , 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 ?? = 3??2+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 lim???1 5??-4- ?? ??-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 ?? = 2??3 + 3??2 - 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 ?? = 4??2 - ??, 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. ?? = tan-1 ?? (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 - 6??2 + 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)
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