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Prove the following f(x)=tan^(-1)(sinx...

Prove the following
`f(x)=tan^(-1)(sinx+cosx)` is strictly decreasing function on `((pi)/(4),(pi)/(2))`.

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MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE 6 (b) (Short Answer Type Questions)
  1. Prove that the function given by f(x) = cos x is (a) strictly decrea...

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  2. Prove the following (i) f(x)=sinx is : (I) strictly increasing in ...

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  3. Prove the following f(x)=tan^(-1)(sinx+cosx) is strictly decreasing ...

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  4. Prove that the logarithmic function is strictly increasing on (0,oo).

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  5. Prove that the function f given by f(x)" "=" "log" "s in" "x f(x)" "="...

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  6. Prove that the function f given by f" "(x)" "=" "log" "cos" "x is stri...

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  7. Show that the function f(x) = x3– 3x^2 + 6x – 100 is increasing on .

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  8. Find the intervals in which the following functions are increasing : ...

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  9. Find the interval in which 2x^(3)+9x^(2)+12x-1 is strictly increasing.

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  10. Find the intervals in which the functions : (i) f(x)=x^(3)+2x^(2)-1 ...

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  11. Prove that the function f(x)=x^2-x+1 is neither increasing nor decr...

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  12. Find the values of 'a' for which the function : f(x)=x^(2)-2ax+6 is in...

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  13. Find the values of 'a' for which f(x)=sinx-ax+b is decreasing function...

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  14. Find the values of x for which y=[x(x-2)]^2is an increasing function

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  15. Determine for which values of x, the following functions are increasin...

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  16. Determine for which values of x, the following functions are increasin...

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  17. Determine for which values of x, the following functions are increasin...

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  18. Determine for which values of x, the following functions are increasin...

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  19. Determine for which values of x, the following functions are increasin...

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  20. For what values of 'x' are the following functions increasing or decre...

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