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Prove the inequality x^2e^(-x^2) le e^...

Prove the inequality
`x^2e^(-x^2) le e^(-1),x in R`.

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The correct Answer is:
`x^(2) e^(-x^(2)) le e^(-1) x in R`
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ARIHANT PUBLICATION-APPLICATION OF DERIVATIVES -ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 8 (D))
  1. Shows that the following functions do not possess maximum or minimum. ...

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  2. Use the function f(x) = x^(1//x), x gt 0 to show that e^(pi) gt pi^(e)...

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  3. Prove the inequality x^2e^(-x^2) le e^(-1),x in R.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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