tutorial5 - to estimate the maximum possible error and the...

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MATH 1007 - TUTORIAL 5 Please work in teams of 4. At the end of the tutorial every team hands in one set of solutions with everybody's name and student number PRINTED, and every- body's signature. Don't worry if you can't finish all the questions; what you haven't finished in class, finish at home. The main goal of the tutorial is to learn by working together. The tutorial problems are intended to be an enjoyable learning experience, not a competition. Anyone regularly participating in tutorials can expect a reasonable grade for the tutorial work. Do NOT divide up the problems between you and work on them separately. Groups doing this will be marked in a tougher fashion. You and your group should work together on all problems sharing insights and difficulties as you progress. Your TA and instructor are here to help you - don't be shy to ask questions! * * * 1. Let f be a one-to-one differentiable function. If f(4) = 5 and f' (4) = 7, find (f-l), (5). Then write down the linear approximation (li~earization) L(x) of -1 f at x = 5 and use it 'to find an approximate value for f-l(5~). 2. The edge of a cube was found to be 100 cm with the possible error in measurement of 0.5cm. Use differentials
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Unformatted text preview: to estimate the maximum possible error and the percentage error in computing the volume of the cube. 3. Use I'Hospital's rule to find: x a) lim arctan(4x) x-+O b) lim x2ex x-+-oo c) lim (xe1/x_ x) x-+oo d) lim+ (1 + !)X x-+O x Why doesn't it work? 2 4. What happens when you try to use I'Hospital's rule to compute lim ~ + x + x x-+O ? 5. For the function f(x) = x + cot(x/2) find its absolute maximum and absolute minimum values on the interval [n/3,2n/3]. 6. a) Sketch the graph of a function f on the interval [0,1] which has no absolute maximum on [0,1] but has a local maximum at x = 1. b) Sketch the graph of a function f on the interval (0,3) which has neither a local maximum nor a local minimum, is continuous, and for which 1 and 2 are critical points. * * *...
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This note was uploaded on 03/22/2010 for the course MATH 1007 taught by Professor Unknown during the Fall '07 term at Carleton.

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