Show that the height of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is  Also find the maximum volume. 

Find the equation of the normal at a point on the curve x² = 4y which passes through the point (1, 2). Also, find the equation of the corresponding tangent.

Write the degree of the differential equation 

If a unit vector  and  are two equal vectors, then write the value of x+y+z.

If a unit vector  makes angle  then find the value of .

Find the Cartesian equation of the line passes through the point (-2, 4, -5) and is parallel to the line 

The amount of pollution content added in air in city due to x-diesel vehicles is given by  Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above questions.

Show that the function f in 

Differentiate the following function with respect to x:

20.