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Using monotonicity prove that (x)/(1...

Using monotonicity prove that
`(x)/(1-x^(2)) lt tan^(-1)x lt x ` for every `x ge 0`

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MOTION-MONOTONOCITY-Exercise - 3 ( Subjective )
  1. Find the intervals of monotonocity for the following functions & repre...

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  2. Let f(x)={:{(x^(2),x ge 0),(ax, x lt 0):}. Find real values of a such...

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  3. If f(x) = x^(3) + (a – 1) x^(2) + 2x + 1 is strictly monotonically in...

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  4. Find the values ' a ' for which the function f(x)=(a+2)x^3-3a x^2+9a x...

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  5. Find the greatest & least value of f(x)=sin^(-1).(x)/(sqrt(x^(2)+1)...

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  6. Using monotonicity prove that x lt - ln (1-x) lt x (1-x)^(-1) for ...

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  7. Using monotonicity prove that (x)/(1-x^(2)) lt tan^(-1)x lt x for...

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  8. Prove that tan^2x+6lns e c x+2cosx+4>6secx for x\ in ((3pi)/2,\...

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  9. Verify Rolles theorem for the function f(x)=log{(x^2+a b)/(x(a+b))}...

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  10. Using Rolle's theorem prove that the equation 3x^2 + px - 1 = 0 has th...

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  11. f(x) and g(x) are differentiable functions for 0 le x le 2 such that ...

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  12. Show that the lagranges mean value theorem is not applicable to the...

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  13. If a, b are two real numbers with a lt b show that a real number 'c' ...

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  14. Using LMVT prove that : (a) tan x gt x in (0, pi/2), (b) sin x l...

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  15. Construct the graph of the function f(x)=-|(x^(2)-9)/(x+3)-x+(2)/(x-...

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  16. Show that exactly two real values of x satisfy the equation x^2= xsinx...

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  17. If g(x) is monotonically increasing and f(x) is monotonically decreasi...

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  18. For x in (0, pi/2) identify which is greater (2 sin x + tan x ) or ...

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  19. Using monotonocity find range of the function f(x)=sqrt(x-1)+sqrt(6...

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  20. Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le...

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