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Show that the function f given by f(x)...

Show that the function f given by
`f(x) = tan^(-1) (sin x+cosx ) , x gt 0`
is always an increasing function in `(0,(pi)/(4))` .

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NCERT TAMIL-APPLICATION OF DERIVATIVES-EXERCISE 6.6
  1. Show that the function f given by f(x) = tan^(-1) (sin x+cosx ) , x ...

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  2. Using differentials, find the approximate value of each of the followi...

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  3. Show that the function given by f(x) =(logx)/(x) has maximum at x = e.

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  4. The two equal sides of an isosceles triangle with fixed base b are dec...

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  5. Find the equation of the normal to the curve x^(2) = 4y which passes t...

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  6. Show that the normal at any point θ to the curve x = a costheta + a th...

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  7. Find the intervals in which the function f given by f(x) = (4sin x-2...

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  8. Find the intervals in which the function f given by f(x) =x^(3) +(1)/(...

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  9. The area enclosed by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1...

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  10. A tank with rectangular base and rectangular sides, open at the top is...

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  11. The sum of the perimeter of a circle and square is k, where k is some ...

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  12. A window is in the form of a rectangle surmounted by a semicircular op...

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  13. A point on the hypotenuse of a triangle is at distance a and b from th...

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  14. Find the points at which the function f given by f (x) = (x-2)^(4)(x+1...

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  15. Find the absolute maximum and minimum values of the function f given b...

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  16. Show that the altitude of the right circular cone of maximum volume th...

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  17. Let f be a function defined on [a, b] such that f ′(x) gt 0, for all x...

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  18. Show that the height of the cylinder of maximum volume that can be ins...

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  19. Show that height of the cylinder of greatest volume which can be inscr...

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  20. A cylindrical tank of radius 10 m is being filled with wheat at the ra...

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  21. The slope of the tangent to the curve x=t^(2)+3t-8,y=2t^(2)-2t-5 at th...

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