1. Let F [ry,-y², 2] be a force field and C be the curve given by the parametrization r(t) = [t, 1/t, e-), 1

Extracted text: 1. Let F [ry,-y², 2] be a force field and C be the curve given by the parametrization r(t) = [t, 1/t, e-), 1 <>< 2.="" compute="" the="" work="" done="" by="" f="" in="" a="" displacement="" along="" the="" curve="" c.="" 2.="" compute="" the="" value="" of="" the="" line="" integral="" (2rydx="" +="" (1+="" 32?y?)dy).="" 3.="" compute="" the="" value="" of="" the="" double="" integral="" ffre="" dxdy,="" where="" r="" is="" the="" triangular="" region="" bounded="" by="" the="" lines="" r="" 0,="" y="0," and="" y="2r." 4.="" compute="" the="" value="" of="" the="" double="" integral="" fre-ydxdy,="" where="" r="" is="" the="" region="" bounded="" by="" the="" lines="" y="r," y="2x," and="" the="" curves="" y="1/a" and="" y="3/r." 5.="" let="" c="" be="" the="" unit="" circle="" a?="" +="" y?="1" with="" the="" counterclockwise="" ori-="" entation="" and="" f="" (-y",="" a*).="" compute="" the="" line="" integral="" fe="" f="" dr="" using="" the="" theorem="" of="" green.="" 6.="" compute="" the="" area="" of="" the="" surface="" s="" given="" by="" the="" parametrization="" r(u,="" v)="[u," v,="" u²="" +="" v²]="" and="" defined="" over="" the="" unit="" disc="" r="{(u," v)="" :="" u²+v²="">< 1}.="" 7.="" find="" the="" equation="" of="" the="" tangent="" plane="" to="" the="" surface="" s:="" r(u,="" v)="[-uv," v,="" u]="" at="" the="" point="" a(-1,="" 1,="" 1).="" 8.="" compute="" the="" surface="" integral="" ff,="" f="" nda,="" where="" f="" [a,="" y,="" 2]="" and="" s="" is="" given="" by="" the="" parametrization="" r(u,="" v)="[u," v,="" 1="" –="" u?="" -="" v*]="" over="" the="" region="" r="{(u," v):="" u2="" +="" v²=""><>