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Prove that f(x)=x-sinx is an increasing ...

Prove that `f(x)=x-sinx` is an increasing function.

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BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. Prove that f(x)=x^3 in an increasing function

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  2. Prove that f(x)=x-sinx is an increasing function.

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  3. Find the intervals in which f(x)=x/(logx) is increasing or decreasing.

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  4. Find the values of a for which the function f(x)=(a+2)x^3-3a x^2+9a x-...

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  5. Determine the intervals in which the function f(x)=x^4-8x^3+22 x^2-24 ...

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  6. Find intervals of monotonicity of function : f(x)=(2x)/(1+x^2)

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  7. Find intervals of monotonicity of function : f(x)=ln\ (x^2-2x)

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  8. Find intervals of monotonicity of function : f(x)=(|x-1|)/(x^2)

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  9. If g(x)=f(x)+f(1-x) and f prime prime (x)< 0; 0 <= x <= 1. show that g...

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  10. Separate the intervals of monotonocity for the function f(x)=x^2e^(-x)

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  11. Compute the intervals of monotonicity for the following f(x)=x+ln(...

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  12. Find value of a so that f(x)=a x-s in x\ is monotonic

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  13. Prove that f(x)=2/3x^9-x^6+2x^3-3x^2+6x-1 is always increasing.

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  14. Find least and greatest value of f(x)=e^x^(2-4x+3)\ in [-\ 5,5]

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  15. Find the image of interval [-1,3] under the mapping specified by...

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  16. Find the range of the following functions f(x)=\ sqrt(x-3)+2sqrt(5-...

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  17. Find the range of the following function f(x)=(x^4-x^2-2x+8)/(x^4-x...

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  18. Prove that 2sinx+tanx\ geq3x\ \ (0lt=x<pi/2)

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  19. Find the set of values of x for which the inequality In(1+x)>x/(1+x) ...

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  20. Show that ln\ (1+x)> x-(x^2)/2\ AA\ x\ in (0,oo)

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