Question

x G Answer The Following Muli m Belgium 3-1 Russia: Eden x ■ CBU I Cape Breton Univers resource%2Fcontent%2F1%2Fassig6,MATH 1203-W201 9pdf Due date: Thurs., Mar. 28 Please get an early start on this assignmext. If you have problens then come and see me to get help. Also remember, there are far more marks for procedure than for final answers. Write your solutions neatly and in a then come and see me to get help well organized fashion. Show all work. There are marks for having well organized, clear solutions to the problems All work submitted must be your own work. You are encouraged to work with other stud ents but do not show each other the final work that you intend to subanit. If you collaborate with other students it is a good idea to cite them as sources for your work. You wil learn more from the assignment if you collaborate with others and discuss t You will learn less from the assignment if you copy. This is one of the major just ifications for academic integrity rules. Questions to be handed in for marking 1. Evaluate each of the following simple definite integrals (5a3 dr is going to "lead you by the nose" through the process of evaluating an integral by formally taking hich is a linear function. the appropriate limit of a Riemann sum. We will do one of the simplest possible cases, w Consider the function We wish to ind the area under f(z) from2 to5 (a) You can easily find this area using elementary geometry. So we to do anything more dificult. Draw the graph of the function, showing the area that we are trying to find. might as well know the answer before we try Then use simple geometry to find this area. Riemann sun that is easy to think about. Wite the left Riemann sum, Ls. which approxi- mates the area that we wast. Evaluate it, using a spreadsheet if you want to redace the amouent of time you spend dealing with all those dirty, annoying numbers (c) In the Riemann sun that you just wrote, you anust have had to define soeme width of the rectangles, Ax, and ) Suppose we are instead golng to write some Riemann sua using a lasger number of rectangles, L. What wil . You should have an expression some list of values of z, which would have been {ra. , ze). Write an expression which generates 11 kth number in this list bethe value of Δ2? How do we write z., the kra valtee ofin the list (Po, ai,.mr.)? which a sum (in "signa notat lou" form), w , (e) Now that you know how to write down Ar and zs, write the Riemann sum, L number ol terms in the sum, n. (f) Manipul late the sum you have fromn the previous part of the question to get rid of the all of the summation notation. You will find it usefiul to knxow (in case you've forgotten) that )nt you (s) Use your expression from the M have an expression which is not a sum. It should just be an expression in terms of a f previous part to evaluate La0. L, L Verify that as n gets large the At t sum appesrs to be couverging towards the value that it shoiuld. (h) Tak, the linii a.. → ㆀ of your expression for L%. Verify that it gives the correct ares

Answer 1