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:2013
QUESTION ONE (30 MARKS) a) Replace the Cartesian equation 2 9
+
2 4
= 1 by the equivalent polar equation. (3 Marks) b) Evaluate ) ( sin 0 lim x x x? (3 Marks) c) Given that = 3. Find the extreme values of f on [0, 1] and determine at which number in [0,1] they occur. (4 Marks) d) Evaluate the iterated integral ? ? ? ?3 2 6 2 x x xydydx (4 Marks)
e) ????() = . (5 Marks) f) Given that , = 4 2 2. Find a function f of two variables and a function g of one variable such that = . (3 Marks) g) Given that , = 33 2+2 , find . (6 Marks) h) State the mean value theorem. (2 Marks)
QUESTION TWO (20 MARKS)
a) Let , = 24 62. Find and evaluate at (1,2). (6 Marks)
2
b) Find the
x e x x
x
2
0
1
lim
?? ?
(4 Marks)
c) Let = 1 3
3 + 2. Find a number c in (0,3) such that = (3(0) 30 . (6 Marks) d) = 3 3 on [0,6].(4 Marks)
QUESTION THREE (20 MARKS)
a) ??????? (4 Marks) b) i) Find the Taylor series generated by = 1 = 2. (4 Marks) ii) Show that the series is geometric and converges to 1 . (4 Marks) c) the total resistance R of two resistors connected in parallel is given by 1 = 1 1 + 1 2 . Approximate the change in R if 1 increased from 10 ohms to 10.5 ohms and 2 decreased from 15 ohms to 13 ohms. (4 Marks) d) Show that the point 2, 2 lies on the curve = 2cos2. (4 Marks)
QUESTION FOUR (20 MARKS)
a) i) find the volume of the prism whose base is the triangle in the XY-plane bounded by the and the lines = and = 1 and whose top lies in the plane (,) = 3 . (5 Marks)
ii) Evaluate the double integral dydx yx? ? ? ? 0 2 0 22 cossin (5 Marks) b) i) Define an improper integral. (2 Marks) ii) Evaluate the integral ?? ? 0 2 dxx e x (5 Marks) c) Find the centre of gravity of a solid hemisphere of radius r. (3 Marks)
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