Question

a) Find the exact value of the slope of the line which is tangent to the curve given by the equation

r = 2 + cos θ at . You must show your work.

b) Set up, but do not evaluate, the integral that represents the length of the curve given by

x = t - t², , over the interval 1 ≤ t ≤ 2.

D 4,3/2 y=7

Answer 1

(a) theu dy өP Jup bt (2tCole) +Cos o ars-2sihg - 2 Sino COJO do (2.t coso)sine я sino -2 Sino t CoJO sin 2 cojo co0 -si,o dy 2 Coso tCos 2 2o eao - Sin2o 260S II Coj T sin T L 2 2 2

(b) 2 di 12* 3 is SonLengt betweeu fA2 dx dt dt dy dt ( This tn set up doitfurthen) clt -2a)2