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Show that the minimum distance of a poin...

Show that the minimum distance of a point on the curve `(a^(2))/(x^(2)) + (b^(2))/(y^(2)) = 1` from the origin is a + b.

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Find the minimum distance of a point on the curve 2/x^2+1/y^2= 1 from the origin.

Find the equation of the tangent and normal to the curve (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 at the point (sqrt(2)a, b) .

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Show that the condition that the curves ax^(2) + by^(2) = 1 and a_(1)x^(2) + b_(1)y^(2) = 1 should intersect orthogonally such that (1)/(a) - (1)/(b) = (1)/(a_(1)) - (1)/(b_(1)) .

Find the condition for the curves (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 and xy = c^(2) to intersect orthogonally.

ARIHANT PUBLICATION-APPLICATION OF DERIVATIVES -ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 8 (D))
  1. Prove the inequality x^2e^(-x^2) le e^(-1),x in R.

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  2. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  3. Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.

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  4. Determine the absolute maximum and absolute minimum of the following f...

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  5. Find extreme value of f(x).={{:((x)/(1-x^2),-1ltxlt0),(x^3-x,0lexlt2):...

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  6. Find two numbers x and y whose sum is 15 such that xy^2 is maximum.

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  7. If then sum of two positive numbers in constant then show that their p...

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  8. Determine a rectangle of area 25sq. Units which has minimum perimeter.

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  9. Find the altitude of a right circular cylinder of maximum volume inscr...

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  10. Show that the radius of the right cicular cylinder of greatest curved ...

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  11. Show that the semivertical angle of a cone of given slant height is ta...

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  12. A cylindrical open water tank with a circular base is to be made out o...

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  13. A cylindrical vessel of capacity 500 cubic metres open at the top is t...

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  14. Find the coordinates of the point on the curve x^2y - x + y = 0 wher...

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  15. Find the points on the curve y = x^2+1 which are nearest to the point ...

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  16. Show that the minimum distance of a point on the curve (a^(2))/(x^(2))...

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  17. Show that the vertical angle of a right circular cone of minimum curve...

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  18. Show that the semi-vertical angle of a right circular cone of minimum ...

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  19. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

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  20. Shows that the triangle of greatest area that can be inscribed in a ci...

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