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Prove that x/(1+x)>ln(1+x)< x AA x>0...

Prove that `x/(1+x)>ln(1+x)< x AA x>0`

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BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. Show that ln\ (1+x)> x-(x^2)/2\ AA\ x\ in (0,oo)

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  2. Show that the equation x^5-3x-1=0\ has a unique root in [1,2] .

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  3. Prove that x/(1+x)>ln(1+x)< x AA x>0

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  4. f( x )=cos3x−15cosx+8  in  [ π/ 3 , 3π/ 2 ] is increasing or ...

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  5. Use the function f(x)=x^(1/x),x >0, to determine the bigger of the two...

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  6. Prove that e^x-e^(-x)-2x >0\ AA\ x > 0. Hence, prove that e^x+e^...

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  7. prove that the function f(x)=(lnx)/x , is strictly decreasing in...

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  8. Verify Rolles Theorem for f(x)=(sin x)/(e^x)\ in\ [0,pi]\ \ \ \ ...

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  9. Find c of L M V T f(x)=\ sqrt(x-1)\ \ " in "\ [1,3]

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  10. Using Lagranges mean value theorem, prove that |cosa-cosb|<=|a-b|dot

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  11. Verify Rolles theorem for the function f(x)=(x-a)^m(x-b)^n on the inte...

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  12. Let f(x)=4x^3-3x^2-2x+1, use Rolles theorem to prove that there ...

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  13. Let f be a twice differentiable function on [0,2] such that f(0)...

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  14. Find the value of a , if the equation x-sinx=a has a unique r...

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  15. Find the intervals in which the given function increases or decreas...

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  16. Prove the following inequalities 1+cotx\ lt=cotx/2\ AA\ x in (0,pi)

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  17. Leg f(x)=x^3+a x^2+b x+5sin^2x be an increasing function on the set Rd...

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  18. Find the values of x where f(x)=sin(lnx)-cos(lnx) in strictly increasi...

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  19. Prove that sin^2theta<thetasin(sintheta)for0<theta<pi/2dot

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  20. Let f: R->R be a function such that f(x)=a x+3sinx+4cosxdot Then f(x...

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