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If the area of a circle increases at a u...

If the area of a circle increases at a uniform rate, then prove that perimeter varies inversely as the radius.

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The correct Answer is:
`(dP)/(dt)prop (1)/(r )`
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KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)
  1. A spherical ball of salt is dissolving in water in such a manner that ...

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  2. If the area of a circle increases at a uniform rate, then prove that p...

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  3. A kite is moving horizontally at a height of 151.5 meters. If the spee...

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  4. Two men A and B start with velocities v at the same time from the junc...

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  5. Find an angle theta, where 0 lt theta lt (pi)/(2) which increases twic...

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  6. Find the approximate value of (1.999)^(5).

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  7. Find the approximate volume of metal in a hollow spherical shell whose...

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  8. A man, 2m tall, walks at the rate of 1(2)/(3) m/s towards a street lig...

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  9. A swimming pool is to be drained for cleaning. If L represents the num...

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  10. The volume of a cube increases at a consant rate. Prove that the incre...

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  11. x and y are the sides of two squares such that y=x-x^(2). Find the rat...

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  12. Find the condition that the curves 2x=y^(2) and 2xy = k intersect orth...

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  13. Show that the curves xy=a^(2) and x^(2)+y^(2)=2a^(2) touch each other.

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  14. Find the co-ordinates of the point on the curve sqrt(x)+sqrt(y)=4 at w...

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  15. Find the angle of intersection of the curves y = 4-x^(2) and y=x^(2).

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  16. Prove that the curves y^(2)=4x and x^(2)+y^(2)-6x+1=0 touch each other...

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  17. Find the equation of the normal lines to the curve 3x^(2)-y^(2)=8 whic...

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  18. At what points on the curve x^(2)+y^(2)-2x-4y+1=0, the tangents are pa...

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  19. Show that a point at which the line (x)/(a)+(y)/(b)=1 touches to the c...

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  20. Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) is increasing in R.

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