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) Convert the following polar equation to the equivalent Cartesian equation ?? = cos?? + sin??. (3 Marks) b) Find the polar equation equivalent to the Cartesian equation ??2 25 + ??2 4 = 1 . (3 Marks) c) Given ?? ?? = ?? - ??3. Find the extreme values of g on [0,1] and determine at which number in [0,1] they occur. (4 Marks) d) State the mean value theorem. (2 Marks) e) Evaluate the iterated integral ????2???????? ?? ??=?? 1 ??=0 (4 Marks) f) Given that ?? ??,?? = ??3??-????3 ??2+??2 find ?? ?? and ?? ??. (6 Marks) g) Find the lim???0 ????-??-1 ??2 . (3 Marks) h) Find the Mac Laurin’s series generated by ?? ?? = ????. (5 Marks)
QUESTION TWO (20 MARKS) a) Show that the point (2,?? 2 ) lies on the curve ?? = 2cos2??. (4 Marks) b) Find the Cartesian equivalent of the polar equation. ??cos ?? - ?? 6 = 3. (4 Marks) c) Define the Taylor’s and Maclaurin’s series generated by a function f. (4 Marks)
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d) i) Find the Taylor series generated by ?? ?? = 1 ??
at ?? = 2. (4 Marks) ii) Show that the series is geometric and converges to 1 ?? . (4 Marks)
QUESTION THREE (20 MARKS)
a) Given that ?? ??,?? = ln? (4 - ??2 - ??2). Find a function f of two variables and a function g of one variable such that ?? = ??????. (6 Marks) b) Let ?? ??,?? = 24???? - 6??2??. Find ?? ?? and ?? ?? and evaluate them at (1,2). (6 Marks) c) Find the domain of the function ?? ??,?? = ??2 + ??2 - 25. (4 Marks) d) Let ?? ?? = 1 3 ??3 + 2??. Find C in (0,3) such that ??' ?? = ?? 3 -??(0) 3-0 . (4 Marks)
QUESTION FOUR (20 MARKS)
a) i) define the improper integral of non negative f. (2 Marks) ii) Evaluate ????-2?????? 8 0 . (5 Marks) b) By first changing the Cartesian integral to the equivalent polar integral, evaluate ??2 + ??2 ???????? ??2-??2 0 ?? 0 (5 Marks) c) Find the centre of gravity of a lamina bounded by the parabola ?? = ??2 and the line ?? = ?? + 2. (8 Marks)
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