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Prove that |cosalpha-cosbeta|lt=|alpha-b...

Prove that `|cosalpha-cosbeta|lt=|alpha-beta|`

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CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. Prove that ln(1+x) < x for x > 0.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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