I need help with question 22!

Suppose a cable hangs from the point A to the origin, as in Figure 9. 11 and has a uniformly clistributed load of p pounds per fout Suppose gis the tension force at O. Assume futhermore that they Coordinate of A is x . Then the cable traces out the parabolic cure given by 2 f ( t ) = pt 29 for OLZ LX so that in particular , 2 PX 29 a . Show that the length of of the cable is given by 712 ) pin 2nt 1 2n+1 9zn b. Determine the radius of convergence of the series given ina. O X Figure 9.11 uniformly loaded cable574 9 SEQUENCES AND SERIES integrating the power series term by term. In each part pounds per foot. Suppose q is the tension force at 0. below, use Newton's ideas to carry out the integration, Assume furthermore that the x coordinate of A is x. Then and then determine the radius of convergence of the the cable traces out the parabolic curve given by resulting power series. Take a > 0. a . "Vaz + 1 2 di b . [Va - 1 2 dl S (t ) = for O S t s x 29 18. a. Find the numerical values of () and (1/2) so that in particular, b. Show that A = x, 29 a. Show that the length & of the cable is given by for any positive integer s. (Hint: Use (2).) c. Show that E. ( ) -1X -0 p 2m 2n + 1 920 gen X 2n+ 1 for any positive integer s. (Hint: Use (2).) b. Determine the radius of convergence of the series 19. Prove that if |s| $ 1 and n 2 1, then given in (a). 23. Suppose a suspension bridge has span a and sag b (Fig ure 9.12). Then it can be shown that the length & of the supporting cables is given by 20. The first partial sum 1 + x/2 of the binomial series for (1 + x)1/2 is often used as an approximation of (1 + x) 1/2. sp = 2 1 + 6462 1/2 Using the Lagrange form of the remainder r, (x), show a4 dx that the error introduced is at most (0.172)x, provided that |x|