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A window has the shape of a rectangle su...

A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 m, find the dimensions of the rectangle that will produce the largest area of the window.

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
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  2. Let AP and BQ be two vertical poles at points A and B respectively. If...

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  3. A window has the shape of a rectangle surmounted by an equilateral tri...

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  4. Find the rate of change of area of a square when its side is increasin...

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  5. If the rate of change of volume of a sphere is numerically equal to th...

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  6. If the area of a circle increases at a uniform rate, then prove that t...

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  7. Find a real number theta, 0 < theta < pi/2, which increases twice as f...

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  8. Find the rate of change of perimeter of a square when its side is incr...

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  9. Find the rate of change of perimeter of a square when its side is incr...

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  10. Find the rate of the change of surface area of a sphere when its radiu...

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  11. The volume of a cube is increasing at a constant rate. Prove that the ...

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  13. The rate of change of the volume of a sphere w.r.t. its surface area, ...

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  14. Prove that the function f(x) = tanx-4x is strictly decreasing on (-pi/...

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  15. Find the interval in which the function f(X) = x^4 - (4x^3)/(3) is str...

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  16. Show that the function f given by f(x) = tan^-1(sinx+cosx), x>0 is alw...

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  17. State whether the function f(x) = x^3 is increasing or decreasing.

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  18. State whether the function f(x) = e^x is increasing or decreasing.

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  19. Is the function y = cot x decreasing on the interval (0,pi)?

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  20. Find the interval of increase of the function f(x) = tan^-1 x.

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