Answer 58 and 59 58. Find the slope of the tangent line at (-1,1,5) to the curveof intersection of the surface z = x+4y2 and(a) the plane x =-12(b) the plane y = 1.59. The volume V of a right circular cylinder is given by theformula V = Tr'h, wherer is the radius and h is theheight.the ingtontoneous rate ofchange

According to question, we have, z = x2 + 4y2 .......(1)58 . (a). The plane x = -1, put the value of x = -1 in equation (1), we get, z = (-1)2 + 4y2,z = 4y2 +1,now,differentiate above equation with respect to 'y',we get,dzdy = 8 y,now,We need to calculate slope of tangent at -1,1, 5,we get,dzdy-1,1, 5 = 8 ×1,dzdy-1,1, 5 = 8 Answer,This is the required slope of tangent at -1,1, 5 with the intersection of plane x = -1.58. (b). The plane y= 1, put the value of y = 1 in equation (1), we get, z = (x)2 + 412,z = x2 +4,now,differentiate above equation with respect to 'x',we get,dzdx = 2x,now,We need to calculate slope of tangent at -1,1, 5,we get,dzdx-1,1, 5 = 2×-1,dzdx-1,1, 5 = -2 Answer,This is the required slope of tangent at -1,1, 5 with the intersection of plane y=1. Question no. 59 is not complete question, it seems to be objective of question is missing, please post complete question, separately, we are happy to guide you.