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Show that x/(1+ x tan x,) x in (0,pi/2)i...

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

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MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-PROBLEM
  1. Find the equation of the tangent and normal to [x/a]^(1/3)+[y/b]^(1/3)...

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  2. Show that the function e^x/x^p is strictly increasing for x gt p gt 0.

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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. Find the extreme values of y = cos x(1+sin x), x in [0,2pi]

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  5. Find the equation of normal to the curve x^3 =4y which passes through ...

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  6. Prove that y=mx+c touches the parabola y^2 = 4ax if a=mc.

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

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  8. Find the intervals where the following functions are (a) increasing an...

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

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  10. Find the values of x for which f(x) = x^4+2x^3-2x^2-6x+5 is locally ma...

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  11. Show that the tangent to the curve y=x^2+3x-2 at (1,2) is parallel to ...

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

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  13. Show that y=mx+c is a tangent to the ellipse x^2/a^2+y^2/b^2=1 if c^2=...

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  14. A square piece of tin of side 18 cm is to be made into a box without t...

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  15. Show that the equation of the normal to x^(2/3) + y^(2/3) = a^(2/3)is ...

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  16. Find the interval where y=sin2x-cos2x,xin[0,2pi] is (a) incresing (b)...

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

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

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  19. Find the condition that the line x cos alpha+y sin alpha = P mam be a ...

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

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