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Using Lagranges mean value theorem, prov...

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

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BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. Verify Rolles Theorem for f(x)=(sin x)/(e^x)\ in\ [0,pi]\ \ \ \ ...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. f(x)=(x-2)|x-3| is monotonically increasing in (a)(-oo,5/2)uu(3,oo)...

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  15. A function g(x) is defined as g(x)=1/4f(2x^2-1)+1/2f(1-x^2)a n df(x) ...

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  16. Let f(x)=1-x-x^3.Find all real values of x satisfying the inequality,...

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  17. The intervals of increase of f(x) defined by f(x)=int(-1)^x(t^2+...

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  18. If mean value theorem holds good for the function f(x)=(x-1)/x on ...

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  19. Let f(x)a n dg(x) be two continuous functions defined from RvecR , suc...

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  20. Find the critical points of the function f(x)=2/3sqrt(x^3)-x/2+int1^x(...

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