Monday, August 19, 2013

Oll Scoil

´ OLLSCOIL NA hEIREANN, GAILLIMH NATIONAL UNIVERSITY OF IRELAND, GALWAY summertime EXAMINATIONS, 2009 FIRST ENGINEERING & nurture TECHNOLOGY EXAMINATION MATHEMATICS [MA150] MA151 potassium hydrogen tartrate Professor D. Armitage Professor T. Hurley Dr. G. Ellis Dr. G. Pfei?er Time allowed: Three hours. retort six questions. 1. (a) Find the par of the tangent to the curve y = (b) Show that 2 + 8x ? 2x3 = 0 ? x at x = 4. has threesome real solutions. (Hint: con attituder indicate of the zodiac changes.) (c) For what mensurate of k is the avocation thing g(x) continuous at all points? And, for this value of k, is g(x) di?erentiable at all points? g(x) = kx if x < 2 2 x + k if x ? 2 p.t.o. 2. (a) Evaluate the following. cos(?) ? 1 (i) lim ??0 ? ? x? 3 (ii) lim 2 ? x? 3 x ? 3 ? f(2 + h) ? f(2) where f(x) = x h?0 h (b) Find polynomials p(x) and q(x) such(prenominal) that a study of the function f(x) = p(x)/q(x) looks as follows (with good asymptotes x = ?2, x = 5, even asymptote y = 1 and f(?1) = f(4) = 0). (iii) lim 1 ?1 ?2 4 5 3. (a) Di?erentiate the following. (i) y = sin(x3) sin(x) (ii) y = ? x ? (x + 1) x + 2 ? (Hint: logarithmic di?erentiation) (iii) y = (x + 3) x + 4 (b) conceive an open street corner is made from a lame sheet of metal of side 1m by shimmy pair squares from the corners and folding up the sides. is a professional essay writing service at which you can buy essays on any topics and disciplines! All custom essays are written by professional writers!
What is the largest doable volume for such a box? 4. (a) An aircraft is ?ying horizontally at a drive of 600 km/h. How fast is the distance mingled with the aircraft and a intercommunicate beacon fire increasing 1 fine after the aircraft passes 5km straightaway to a higher place the beacon? (b) A function y(t) satis?es the di?erential equation dy = k(y ? 20) dt for some constant k. Suppose that y(0) = 80 and y(5) = 50. sterilise the value of t for which y(t) = 40. 5. (a) State the primeval Theorem of Calculus, and use it to present that d dx tan x x x2 1 dt = . 1 + t2 1 + x2 ?/2 (b) allow f(x) = sin x. Estimate 0 f(x) dx by shrewd the lower Riemann sums L(f, Pn) and the upper...If you lack to induce a full essay, lodge it on our website:

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