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Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x...

Show that `f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x)` is increasing on `R` .

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RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTION -All Questions
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  2. Prove that the function f(x)=tanx-4x is strictly decreasing on (-pi//3...

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  3. Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) is increasing on R .

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  4. Test whether the function f(x)=x^3-8 is increasing on [1,\ 2] .

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  5. Which of the following functions are decreasing on (0,\ pi//2) ? (i) c...

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  7. On which of the following intervals, the function x^(100)+sinx-1 is...

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  10. If a ,\ b ,\ c are real numbers, then find the intervals in which f(...

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  11. Show that for ageq1,\ \ f(x)=sqrt(3)sinx-cosx-2a x+b is decreasing on ...

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  12. Show that f(x)=cos(2x+pi//4) is an increasing function on (3pi//8,\ 7p...

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  13. Find the least value of ' a ' such that the function f(x)=x^2+a x+1 is...

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

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  17. Find the intervals in which f(x)=x^2+2x-5 is increasing or decreasing.

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  18. Find the intervals in which f(x)=6-9x-x^2 is increasing or decreasing.

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  19. Find the intervals in which f(x)=2x^3-12 x^2+18 x+15 is increasing or ...

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  20. Find the intervals in which f(x)=5+36 x+3x^2-2x^3 is increasing or dec...

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