applied math, management homework help

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I want the answer for two questions q 16 from book and the other one from paper about the extremal function. also , I uploaded exampels and rule that help to answer questions.

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m 1 urve existe X = = 2C16 - sin ®) + ca, V2 y = Yi + 1 28 29(1 - cos $), C2 are constants to be determined such that P, and P, are on the cury [The extremals are cycloids. It is known that Ci and c, can be uniquely dete mined so that P, and P, are on the same “arch" of one such cycloid and that corresponding arc P,P, then truly minimizes T.] Section 2.4. 16. Determine the stationary functions associated with the integral I= - S (yº2 -- 2ayy' - 2By') dx, where a and B are constants, in each of the following situations: (a) The end conditions y(O) = 0 and y(1) = 1 are preassigned. (b) Only the end condition y(0) = 0 is preassigned. (c) Only the end condition y(1) 1 is preassigned (d) No end conditions are preassigned. Note any exceptional cases. 17. Determine the natural boundary conditions associated with the determi tion of extremals in each of the cases considered in Problem 9. #1 Page 196 Problem 16. #2 Consider the functional Jy (3) = "- d.o. Find the extremal of J(y) when (a) y(0) = 1/2, y(7/4) = 1, (b) y(0) = 1/2 and y(7/4) is unassigned. c) y(0) is unassigned and y(7/4) = 1 d) both y(0) and y(7/4) are unassigned. | | o- - - - o - Б - - P, 2 - - со (f2= ifs С : Сс Rift, h =liffhof paisipadoun (1) \: ( lolf Xp (ght (я 2 Extermite — А о- (м) Р'») Pe о пэн\ - - - - nə әF\ ? 5, 25 - 5 ) - о 15 - - () 25 - - 25 х 25 =(n So +S - (xof 0=(1) fe = = ( 2 - MMQUELIUS ка о 2 x-st ta '=(xif tary 7 1=X — life is — (1),fi (11fu (0) SC - 54-5- C- 25 + - txt. JORDI LABANDA - О (9) - Go (Qo'q) с (С) о- to ks us\nә лә-ләЧІ fossips fshiu (kih udut pain-ed osh unfunf o finy The (тело (0) Afox No 4 alla - uoltip uo әл әsә че Ejounoa hunfon paino So uѕitечо) JORDI L
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Really helpful material, saved me a great deal of time.

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