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Find the rate of change of the area of a circle with respect to its radius r when(a) `r = 3 c m` (b) `r = 4 c m`

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To find the rate of change of the area of a circle with respect to its radius \( r \), we can follow these steps: ### Step 1: Write down the formula for the area of a circle. The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] ...
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NCERT ENGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.1
  1. The total revenue in Rupees received from the sale of x units of a pr...

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  2. A balloon, which always remains spherical, has a variable diameter 3/...

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  3. The radius of an air bubble is increasing at the rate of 0.5 cm/sec...

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  4. A particle moves along the curve 6y = x^(3)+2. Find the points on th...

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  5. A ladder of length 5 m is leaning against a wall. The bottom of ladde...

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  6. The rate of change of the area of a circle with respect to its radius...

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  7. The total revenue in Rupees received from the sale of x units of a pr...

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  8. The total cost C (x) in Rupees associated with the production of x uni...

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  9. Sand is pouring from a pipe at the rate of 12 c m^3//s . The falling s...

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  10. An edge of a variable cube is increasing at the rate of 3cm per second...

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  11. A stone is dropped into a quiet lake and waves move in circles at the ...

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  12. The radius of a circle is increasing at the rate of 0.7 cm/s. What is...

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  13. The length x of a rectangle is decreasing at the rate of 5 cm/minute ...

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  14. Find the rate of change of the area of a circle with respect to its r...

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  15. The volume of a cube is increasing at the rate of 8 c m^3//s. How fast...

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  16. The radius of a circle is increasing uniformly at the rate of 3 cm/s....

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  17. A balloon, which always remains spherical on inflation, is being infl...

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  18. A balloon, which always remains spherical, has a variable radius. Fin...

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