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Your answer must be provided with descriptions how to get the answer.1. (5 points) Find the maximum rate of change of the function

sin at the point .

2. (5 points) Find the volume of the solid bounded by the first octant of the plane , the paraboloid , and inside the cylinder .

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3.(6 points) Find an equation of the plane that passes through the point and cuts off the smallest volume in the first octant.

4.(6 points) Find the area of surface with the vector equation sinhcos sinhsin , ln , .

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5.(6 points) Evaluatesin , where is the circular

helix given by the equations cos sin , .

6. (6 points) Evaluate the line integral ,

where is the cycle .

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7. (6 points)

!Find the work done by the force field in moving a particle along the ellipse " " with counterclockwise orientation.