integral and differential calculus related assignmentNirma

integral and differential calculus related assignment
Nirma University
Institute of Technology
Department of Mathematics
B. Tech. (ALL) – Semester – II Calculus (2MA101)
Assignment – 2
Q 1 Find the maxima and minima of the functionf x,y? ?? y x2 3?12? ?3x 4y?.
Q2 A rectangular box open at the top is to have a volume 108 cubicmeters. Find the dimension of the box if its total surface area is minimum.
Q3 Find the maxima and minimum distance from the origin to the curve 3×2 ? 4xy?6y2 ?140using Lagrange’s multiplier method.
Q4 Expand sin(x + y) about origin.
Q5 Find the equations of the tangent and normal to the curve y ? 2×2 ?4x ?5at the point (3, 11).
Q 6 ??u,v,w?
Find the Jacobian for the functionsx ? u, y ? utanv,z ? w.
??x,y,z?
Q 7
3 x1 dx
Solve ?dx??
0 3?x 0 1?x14
Q 8 Find the area of the surface of revolution generated by revolving the curve x ? y3 about y axis from y=0 to y=2.
Q 9 Find the volume of the solid generated by revolving the region bounded by the curve y ?logx and x=2 about the x axis.