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Show that the curves 2x = y^2 and 2xy = ...

Show that the curves `2x = y^2` and `2xy = k` cut at right angles if `k^2 = 8`.

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MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. If the curves: alphax^2 + betay^2 =1 and alpha'x^2 + beta'y^2=1 inters...

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  2. Prove that the curves 4x = y^2 and 4xy = k cut at right angles if k^2...

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  3. Show that the curves 2x = y^2 and 2xy = k cut at right angles if k^2 =...

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  4. Prove that the curves y^(2)=4axandxy=c^(2) cut at right angles if c^(4...

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  5. Show that the normal at any point theta to the curve x = a cos theta +...

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  6. Find the equations of the tangent and normal to the curve 16x^2 + 9y^2...

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  7. Find a point on the curve y=x^(3), where the tangent to the curve is p...

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  8. Find a point on the parabola y =(x-3)^2, where the tangent is parallel...

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  9. Show that the area of the triangle formed by the tangent and the norma...

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  10. Find the equations of the normal at a point on the curve x^2=4y, which...

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  11. Find the equations of the tangents to the curve 3x^2 - y^2 = 8, which ...

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  12. Determine the values of 'x' for which the function f(x) = x^2 + 2x - 3...

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  13. Determine the intervals in which the function f(x) = (x-1)(x+1)^2 is i...

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  14. Using differentials, find the approximate value of sqrt26

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  15. Using differentials, find the approximate the value of root3(0.026) up...

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  16. Find the approximate change in the volume V of a cube of side x metres...

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  17. If the radius of a sphere is measured as 9 m with an error of 0.03 m, ...

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  18. If y = x^4 + 10 and x changes from 2 to 1.99, find the approximate cha...

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  19. Use differentials to calculating approximate value of loge(9.01)

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  20. Use differentials to find the approximate value of tan46^@, if it is b...

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