The amount of pollution content added in air in a city due to x-d i e s e l vehicles is given by` P(x)=0. 005 x^3+0. 02 x^2+30 xdot` Find the arginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.

The total cost C(x) associated with product of 'x' units of an item is given by: C(x) =0.005 x^3-0.02x^2 + 30 x + 500 . Find the marginal cost when 3 units are produced.

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x^3 - 0.02 x^2 + 30x + 5000 Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

Find the intervals in which the function given by f(x) = sin 3x , x in [ 0, pi/2 ] is increasing.

The money to be spend for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (Marginal revenue). If the total revenue (in rupees) received from the sale of x units of a product is given by R(x)=3x^2+36 x+5 , find the marginal revenue, when x=5, and write which value does the question indicate.

Find the particular solution of the differential equation (1+x^2)(dy)/(dx)l=e^(mtan^-1x)-y given that y=1 when x=0

If t is a real number satisfying the equation 2t^3-9t^2+30-a=0, then find the values of the parameter a for which the equation x+1/x=t gives six real and distinct values of x .

Determine the values of 'x' for which the function f(x) = x^2 + 2x - 3 is an increasing. Also find the co-ordinates of the points on thecurve y = x^2 + 2x-3 , where the normal is parallel to the line x - 4y + 7 = 0

A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation sqrt3 x+ y -6 = 0 and the point D is (3 sqrt3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ. The equation of circle C A. y=(2)/(sqrt3)+x+1,y=-(2)/(sqrt3)x-1 B. y=(1)/(sqrt3)x,y=0 C. y=(sqrt3)/(2)x+1,y=-(sqrt3)/(2)x-1 D. y=sqrt3x,y=0

Given that (dy)/(dx)=e^(-2y) and y=0 when x=5. Find the value of x when y=3.

Let g(x)=2f(x/2)+f(2-x) and f''(x) < 0 AA x in (0,2). If g(x) increases in (a, b) and decreases in (c, d), then the value of a + b+c+d-2/3 is