8. A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening. Application of…
7. The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle. Application…
6. A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m3. If building of tank costs Rs 70 per sq metres for…
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 one end of the major axis. Application of Derivatives Miscellaneous Exercise Previous Next Class 12 Application of Derivatives Miscellaneous Exercise 1. Show…
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 Derivatives Miscellaneous Exercise Previous Next Class 12 Application of Derivatives Miscellaneous Exercise 1. Show that the function given by (fleft(xright)=frac{log{x}}{x}) has maximum…
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 of Derivatives Miscellaneous Exercise Previous Next Class 12 Application of Derivatives Miscellaneous Exercise 1. Show that the function given by (fleft(xright)=frac{log{x}}{x}) has…
2. The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?…
1. Show that the function given by (fleft(xright)=frac{log{x}}{x}) has maximum at x=e. Application of Derivatives Miscellaneous Exercise Previous Next Class 12 Application of Derivatives Miscellaneous Exercise 1. Show that the function given by (fleft(xright)=frac{log{x}}{x}) has maximum at x=e. 2.…
22. If (y=e^{a{cos}^{-1}{x}}), (-1le xle1), show that (left(1-x^2right)frac{d^2y}{dx^2}-xfrac{dy}{dx}-a^2y=0). Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises 1 to 11. 1. (left(3x^2-9x+5right)^9). 2. ({sin}^3{x}+{cos}^6{x}). 3. (left(5xright)^{3cos{2}x}). 4. ({sin}^{-1}{left(xsqrt…
21. If (y=left|begin{matrix}fleft(xright)&gleft(xright)&hleft(xright)\l&m&n\a&b&c\end{matrix}right|), prove that (frac{dy}{dx}=left|begin{matrix}f'(x)&g'(x)&h'(x)\l&m&n\a&b&c\end{matrix}right|). Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability Miscellaneous Exercise Differentiate w.r.t. x the function in Exercises 1 to 11. 1. (left(3x^2-9x+5right)^9). 2. ({sin}^3{x}+{cos}^6{x}). 3. (left(5xright)^{3cos{2}x}). 4. ({sin}^{-1}{left(xsqrt xright)}),(0le xle1).…
