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

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

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. Show that the function f (x) = (x)/(1+|x|) is a strict increasing func...

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  2. Show that the function f(x) = x -(1)/(x) is a strict increasing functi...

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

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  4. Show that for a ge1 f(x) = sqrt3 sinx-cosx - 2ax +b is decreasing in R...

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  5. Show that the function f given by f(x) = x^(3) - 3x^(2) + 4x, x in R i...

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  6. Show that f(X) = x^3 - 6x^2 + 18 x + 5 is an increasing function for a...

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  7. Show that the function f(X) = (x^2 - 2x +2) e^x + 3 is an increasing f...

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  8. Show that the function x^2 - x+1 is neither increasing nor decreasing ...

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  9. Indicate the interval in which the function f(X) = cos x, 0lex le2pi, ...

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  10. Prove that the function f(X) = cosx is strictly decreasing (0,pi) and ...

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  11. Determine whether the following function is increasing or decreasing i...

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  12. Prove that the function f(x) = tanx-4x is strictly decreasing on (-pi/...

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  13. Find for which values of 'x', the functions: y =x^4 -(4x^3)/3 is incre...

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  14. Find the intervals in which the function f given by f(x) = 4x^3 - 6x^2...

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  15. Determine the values of x for which the function x + 1/x is strictly i...

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  16. Determine the values of x for which the function 2x^3 - 24x + 5 is inc...

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  17. Determine the intervals in which the function f(x) = x^3 + 5x^2 -1 is ...

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  18. Find the interval in which the function f(X) = 3x^4 - 4x^3 - 12 x^2 + ...

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

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  20. Find the intervals in which the function f(X) = (x-1)^3(x-2)^2 is incr...

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