APPM 1360 Final: appm1360summer2017examfinal_sol
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Summer 2017: (20 pts) consider the curve described parametrically by x(t) = t 2 and y(t) = ln(sec t) with 0 t < /2. Find the length of this curve between the points whose y-coordinates are 0 and 1. Find appropriate values of t. y = dx dt. = 1 and dy dt y = 0 = ln(sec t) = 0 = sec t = 1 = t = 0 ln 2 = ln 2 = ln(sec t) = sec t = 2 = t = 2 (sec t)(tan t) = tan t = s(cid:18) dx dt(cid:19)2 dt(cid:19)2. =p1 + tan2 t = sec t since sec t > 0 for 0 t /4. 0 sec t dt = ln| sec t + tan t|(cid:12)(cid:12)(cid:12) 0: (20 pts) let f (x) = sec x. (a) approximate f (x) with a second degree taylor polynomial centered at a = /4. (cid:4) (cid:4)
