Question

Find the equation of tangent to the curve y = cos (x + y), -2π ≤ x ≤ 0, that is parallel to the line x + 2y = 0.

Two farmers X and Y cultivate only three varieties of rice namely Basmati, Permal and Naura. The sale in rupees of these varieties of rice by both the farmers in the months of September and October are given by the following matrices A and B.

Find the particular solution of the following differential equation. $\cos y\,d x+(1+2e^{-x})\sin y\,d y=0;y(0)={\frac{\pi}{4}}$

Evaluate : $\large\textstyle\int\!{\frac{\ d x}{x(x^{5}+3)}}\,.$

The amount of pollution content added in air in a city due to x-diesel vehicles is given by p(x) = 0·005x³ + 0·02x² + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added.

If C = 0·003x³ + 0·02x² + 6x + 250 gives the amount of carbon pollution in air in an area on the entry of x number of vehicles, then find the marginal carbon pollution in the air, when 3 vehicles have entered in the area.

Find the equations of the tangent and normal to the curve ${\frac{x^{2}}{a^{2}}}-{\frac{y^{2}}{b^{2}}}=1$ at the point $({\sqrt{2}}a,b)$ .