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 3x2 ? 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 ? 2x2 ?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.

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 3x2 ? 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 ? 2x2 ?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.

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