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Show that 0 < xsinx-1/2 sin^2x < ((pi-1)...

Show that `0 < xsinx-1/2 sin^2x < ((pi-1))/2 ,AAx in (0,pi/2) dot`

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. For x > 0 lf x=pi/2, show that x-(x^3)/6 < sinx < x

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  2. Let f(x) be a twice differentiable function for all real values of x a...

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  3. Show that 0 < xsinx-1/2 sin^2x < ((pi-1))/2 ,AAx in (0,pi/2) dot

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  4. The value of c in Lagranges theorem for the function f(x)=logsinx in t...

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  5. Prove that ln(1+x) < x for x > 0.

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  6. If the function f(x)=a x^3+b x^2+11 x-6 satisfies conditions of Rolles...

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  7. Prove that |cosalpha-cosbeta|lt=|alpha-beta|

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  8. A value of 'c' for which the conclusion of mean value theorem holds fo...

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  9. If a , b > 0 a n d 0 < p < 1, then prove that (a+b)^p < a^p+b^pdot

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  10. Each question has four choices, a,b,c and d, out of which only one is ...

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  11. Let fa n dg be differentiable on R and suppose f(0)=g(0)a n df^(prime)...

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  12. The abscissa of the point on the curve sqrt(x y)=a+x the tangent at wh...

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  13. For 0ltxltpi/ 2, prove that cos(sinx)gtsin(cosx)

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

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

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

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

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

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

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