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Prove that x/(1+x)ltlog(1+x)" for "xgt0....

Prove that `x/(1+x)ltlog(1+x)" for "xgt0`.

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SURA PUBLICATION-APPLICATIONS OF DIFFERENTIAL CALCULUS-ADDITIONAL QUESTIONS
  1. If x + y = 8, then the maximum value of xy is

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  2. The curve y=e^(x) is

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  3. lim(xto0)x/(tanx) is

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  4. The statement ''If f has a local extremum at c and if f'( c) exists th...

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  5. Identify the incorrect statement.

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  6. Identify the false statement

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  7. A particle moves in a line so that so that x=sqrtt. Show that the acce...

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  8. A man 2 m high walks at a uniform speed of 5km/hr away from a lamp pos...

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  9. At what point on the curve y=x^(2) on [-2, 2] is the tangent parallel ...

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  10. Find the maximum and minimum values of f(x)=|x+3|AAx inRR.

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  11. Find the intervals of increasing and decreasing function for f(x)=x^(3...

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  12. Prove that x/(1+x)ltlog(1+x)" for "xgt0.

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  13. Find the equation of normal to the cure y=sin^(2)x" at "(pi/3,3/4).

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  14. Verify LMV theorem for f(x)=x^(3)-2x^(2)-x+3 in [0, 1].

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  15. The ends of a rod AB which is 5 m long moves along two grooves OX, OY ...

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  16. A ball is thrown vertically upwards, moves according to the law s=13.8...

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  17. If Rolle's theorem holds for f(x)=x^(3)+bx^(2)+ax+5 on [1, 3] with c=(...

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  18. Find the angle of intersection of the curves 2y^(2)=x^(3)andy^(2)=32x.

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  19. Prove that the semi-vertical angle of a cone of maximum volume and of ...

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  20. Show that the curves 4x=y^(2)and4xy=k cut at right angles if k^(2)=512...

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