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If x in (0, 1) then show that 2x lt ln (...

If `x in (0, 1)` then show that `2x lt ln (((1+x))/((x-1))) lt 2x (1+(x^(2))/(2(1-x^(2))))`.

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AAKASH SERIES-MAXIMA AND MINIMA -Exercise - 8.1 (Long Answer Questions)
  1. Show that the function f(x) = sin x defined on R is neither increasing...

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  2. Find the intervals in which the following functions are strictly incre...

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  3. Find the intervals in which the following functions are strictly incre...

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  4. Find the intervals in which the following functions are strictly incre...

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  5. Find the intervals in which the following functions are stricly increa...

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  6. Find the intervals in which the following functions are strictly incre...

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  7. Find the intervals in which the following functions are strictly incre...

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  8. Find the intervals in which the following functions are strictly incre...

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  9. Find the intervals in which the following functions are strictly incre...

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  10. Show that f(x) = cos^(2) x is strictly decreasing on (0, pi//2).

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  11. Show that x + (1)/(x) is increasing on [1, oo).

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  12. Show that (x)/(1+x) lt ln (1+x) lt x AA x gt 0.

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  13. Show that (x)/(1+x^(2)) lt tan^(-1) x lt x when x gt 0.

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  14. Show that tan x gt x for all x in [0, pi//2).

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  15. If x in (0, pi//2) then show that 2x//pi lt sin x lt x.

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  16. If x in (0, 1) then show that 2x lt ln (((1+x))/((x-1))) lt 2x (1+(x^(...

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  17. At what points the slopes of the tangents to the curve y = (x^(3))/(6)...

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  18. Show that the functions ln""((1+x))/(x) and (x)/((1+x)ln(1+x)) are dec...

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  19. Find the intervals in which the function f(x) = x^(3) - 3x^(2) + 4 is ...

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  20. Find the intervals in which the function f(x) = sin^(4) x + cos^(4) x ...

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