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Prove that for x in [0, (pi)/(2)], sin x...

Prove that for `x in [0, (pi)/(2)], sin x + 2x ge (3x(x + 1))/(pi)`.

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ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that for x in [0, (pi)/(2)], sin x + 2x ge (3x(x + 1))/(pi).

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  2. The least value of alpha in R for which 4ax^2+(1)/(x)ge1, for all xgt ...

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  3. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

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  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

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  5. Let f:(0,oo) to vec R be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , ...

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  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a loca...

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  7. A rectangular sheet of fixed perimeter with sides having their lengths...

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  8. A vertical line passing through the point (h,0) intersects th ellipse ...

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  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

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  10. The total number of local maxima and local minima of the function f(x)...

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  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

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  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

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  13. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

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  14. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

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  15. The length of the longest interval in which the function 3sinx-4sin^3x...

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  16. If f(x)=e^(1-x) then f(x) is

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  17. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

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  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

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  19. If f(x) is a cubic polynomil which has local maximum at x=-1 . If f(2)...

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  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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