[3 Marks] [10 Marks] [4 Marks] Let *3- he the path t) = {3:2, $3,?) I] E t if. 1. a} b} C} d} Calculate e," . ,_| Calculate the equation of the tangent line at t = .-. b.- Show the element of arc length, ds = 2121.! 1H + t2 dt. 1Urdculate the length of \"r. Leave your solution in terms of square roots, ether powers, etc. No need to provide a numerical answer. Evaluate ff ds where ns, 1;, z} = o'er + T: + 353. \"r Let F{a',y,z} = {thaws}. a} b} Directly calculate {i.e., without using Green's theorem, the divergence theorem nor Stokes' theorem} the line integral [ F . ds where t} 2 [cos t,sint,[l} with "'r I} 5 t E 21.- parametrises the unit circle in the z = [1 plane. Directly calculate {i.e., without using Green's theorem, the divergence theorem nor Stokes' theorem} ff curlF~ {EA D where D = \"any, El} -. 3:2 + y"a E 1} denote the unit disc in the z = [1 plane. Using an},r method you like, calculate ff curlF ~ {EA 9 where S = {{$,y, z} -. 312 + \"y"! + z1 = 1,3 Tall} denotes the upper hemisphere. Using Green's theorem, prove the divergence theorem, ff div FdA = f F ~ Nds D - where D is an open region having boundary 7- being aclosed curve with outer pointing normal N