oo r: - = oo: so the sequence n=l 2n 1- diverges.

X = 1 + 4t - t , y = 2 - t ; t = 1. = four- 2t, an d dy dx x t = dyldt dx I dt 2t + 1 . . t cos t + sm t = 4-3tz -Wh - 2t . en t 1 ' (x, y) = ( four, 1) and dy I dx = - ~, so an equa. t ion of the tangent to the curve on the aspect equivalent to t = 1 is y- 1 = -~(x- 4), oq/ = - ~x + 7. five. x = t cos t, y = t sin t; t = 1r. while t = 1r, (x, y) = ( -1r, zero) and dy Idx. = akin to t = 7. (a) x dy . dx . ' dy dy I dt t cos t + sin t -d = tcost+smt, -d = t(-smt)+cost,and-d = d ld = . . t t x x t -t s m t+cost = 1 + ln t, 1r - 1r I( -1) = 1r, so an equation of the tangent to U1e curve on the element is y - zero = 1r[x - ( -1r) ) , or y = 1rx + y = t2 + 2; x=l+ ln t = 1 ::} (1, 3).

Fifty two x 10- on (4, four. 2]. zero 2012 Cengnse U:. vnins. All Rights Rescn-. :d. Moy no longer be: scanned. copied, oc duplicnted. or published 10 o publicly available site, in complete or in·p:ut, SECTION eleven. eleven 15. (a) f(x) n f (n) (x) J (n){1) zero x2/ three 1 1x- l /3 1 2 three 2 _1x- four/ three - g- three . §.. x- 7/3 eight four - ~ x- 10 / three three =. x 213 ~ Ta(x) = 1 + ~(x- 1) - IR3(x)l5 ~ lx - ninety three 2/9 8/27 2! (x - 1) 2 + three! (x - 1) three = 1 + ~(x- 1) -·~(x-I? + 841(x (b) zero four eleven , the place Jj< four >(~)~5 M. Now zero. eight 1) three five x five 1. 2 =?