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Show that x/(1+x)ltlog(1+x)ltxforallxgt0...

Show that `x/(1+x)ltlog(1+x)ltxforallxgt0`.

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. For 0ltxltpi/ 2, prove that cos(sinx)gtsin(cosx)

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  2. In which of the following functions is Rolles theorem applicable? (a)f...

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  3. Show that x/(1+x)ltlog(1+x)ltxforallxgt0.

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  4. A point on the parabola y^2=18 x at which the ordinate increases at t...

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  5. Prove that e^x+sqrt(1+e^(2x))geq(1+x)+sqrt(2+2x+x^2)AAx in R

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  6. Determine the local maxima and local minima of f(x)=(x+1)^2(x-1)^3 is

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  7. Let g(x)=f(logx)+f(2-logx)a n df''(x)<0AAx in (0,3)dot Then find the i...

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  8. Prove that The maximum value of (sqrt(-3+4x-x^2)+4)^2+(x-5)^2(w h e r ...

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  9. Find the points of inflection for (a)f(x)=sinx (b)f(x)=3x^4-4x^3

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  10. Statement 1: If both functions f(t)a n dg(t) are continuous on the clo...

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  11. Discuss monotonocity of y=f(x) which is griven by x=1/(1+t^2) and y=1...

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  12. Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2...

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  13. Find the value of a for which the function (a+2)x^3-3a x^2+9a x-1 decr...

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  14. The angle of intersection between the curves y=[|sinx|+|cosx|]andx^2+y...

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  15. Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreas...

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  16. Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if...

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  17. Discuss the monotonocity of function f(x)=2log|x-1|-x^2+2x+3.

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  18. If the area of the triangle included between the axes and any tangent ...

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  19. Separate the intervals of monotonocity for the function f(x)=3cos^4x+1...

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  20. If the tangent at (x1,y1) to the curve x^3+y^3=a^3 meets the curve aga...

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