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Show that 1+xin(x+sqrt(x^2+1))geqsqrt(1+...

Show that `1+xin(x+sqrt(x^2+1))geqsqrt(1+x^2)` for all `xgeq0.`

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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-JEE Advanced (Archive)
  1. Let f(x)={{:(xe^(ax)",", x le0),(x+ax^2-x^3",",x gt 0):} where a is po...

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  2. Show that 2sinx+tanx≥3x, where 0≤x< π/2 ​

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  3. Show that 1+xin(x+sqrt(x^2+1))geqsqrt(1+x^2) for all xgeq0.

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  4. For a twice differentiable function f(x),g(x) is defined as g(x)=f^(pr...

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  5. For the circle x^(2)+y^(2)=r^(2), find the value of r for which the ar...

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  6. Find a point on the curve x^(2)+2y^(2)=6 whose distance from the line ...

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  7. Suppose f(x) is a function satisfying the folowing conditions: (i)f(...

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  8. Let S be a square of unit area. Consider any quadrilateral which has o...

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  9. Determine the point of maxima and minima of the function f(x)=1/8(log)...

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  10. Let (h , k) be a fixed point, where h >0,k > 0. A straight line passin...

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  11. about to only mathematics

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  12. Which normal to the curve y=x^(2) forms the shortest chord?

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  13. A window of perimeter P (including the base of the arch) is in the ...

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  14. A point P is given on the circumference of a circle of radius r. Chord...

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  15. about to only mathematics

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  16. Let A(p^2,-p),B(q^2, q),C(r^2,-r) be the vertices of triangle ABC. A p...

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  17. Let f(x)=sin^3x+lambdasin^2x ,pi/2<x<pi/2dot Find the intervals in whi...

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  18. Find the coordinates of the point on the curve y=x/(1+x^2) where the t...

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  19. A swimmer S is in the sea at a distance d km from the closest point A ...

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  20. If a x^2+b/xgeqc for all positive x where a >0 and b >0, show that 27 ...

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