Month: August 2024

12. Show that the altitude of the right circular cone of maximum volume that can be inscribed in

11. Find the absolute maximum and minimum values of the function f given by (f(x)=cos^2{x}+sin{x}, xin[0,pi]). Application of

10. Find the points at which the function f given by (f(x)=(x–2)^4 (x+1)^3) has (i) local maxima (ii)

9. A point on the hypotenuse of a triangle is at distance a and b from the sides

8. A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter

7. The sum of the perimeter of a circle and square is k, where k is some constant.

6. A tank with rectangular base and rectangular sides, open at the top is to be constructed so

5. Find the maximum area of an isosceles triangle inscribed in the ellipse (frac{x^2}{a^2}+frac{y^2}{b^2}=1) with its vertex at

4. Find the intervals in which the function f given by (fleft(xright)=x^3+frac{1}{x^3},xneq0) is(i) increasing (ii) decreasing. Application of

3. Find the intervals in which the function f given by (fleft(xright)=frac{4sin{x}-2x-xcos{x}}{2+cos{x}}) is (i) increasing (ii) decreasing. Application