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Find the shortest distance of the point (0, c) from the parabola `y=x^2`, where `0lt=clt=5`.

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To find the shortest distance from the point (0, c) to the parabola \( y = x^2 \), we will follow these steps: ### Step 1: Define the Distance Function The distance \( D \) from the point \( (0, c) \) to a point \( (x, y) \) on the parabola can be expressed as: \[ D = \sqrt{(x - 0)^2 + (y - c)^2} = \sqrt{x^2 + (y - c)^2} \] Since \( y = x^2 \) on the parabola, we can substitute this into the distance formula: ...
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NCERT-APPLICATION OF DERIVATIVES-EXERCISE 6.1
  1. Find the shortest distance of the point (0, c) from the parabola y=x^...

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

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

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  4. The radius of an air bubble is increasing at the rate of 1/2c m//s. A...

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

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  6. A ladder 5 m long is leaning against a wall. The bottom of the ladder...

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

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

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  9. The total cost C (x) in Rupees associated with the production of x un...

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

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  11. An edge of a variable cube is increasing at the rate of 3 cm/s. How f...

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

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

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

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

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  16. The volume of a cube is increasing at the rate of 8 cm^3//s. How fast...

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

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

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

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