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sol v e :1/(x+1)-4/((2+x)^2)>0,x!=-1,-2...

`sol v e :1/(x+1)-4/((2+x)^2)>0,x!=-1,-2`

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1/(x+1)-4/(2+x)^2>0`
`((2+x)^2-4(x+1))/((x+1)(2+x)^2)>0`
`(4+x^2+4x-4x-4)/(x+1)(2+x)^2>0`
`x^2/((x+1)(2+x)^2)>0`
...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Show that f(x)=1/x is decreasing function on (0,oo)dot

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  2. Sol v e :(1-x^2)/(5x-6-x^2)<0

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  3. sol v e :1/(x+1)-4/((2+x)^2)>0,x!=-1,-2

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  4. Sol v e:4x^3-24 x^2+44 x-24 >0

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  5. Find the intervals in which the function f(x)=2x^3+9x^2+12 x+20 is (i)...

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  6. Find the intervals in which f(x)=-x^2-2x+15 is increasing or decreasin...

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  7. Sol v e :(x^2-4x+7)/(x^2-7x+12)lt=2/3dot

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  8. Sol v e(8x^2+16 x-51)/(2x^2+5x-12)>3

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  9. Determine the values of x for which f(x)=x^x , x >0 is increasing or d...

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

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  11. Find the intervals in which the function f(x)=x^4-(x^3)/3 is increasin...

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

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

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  14. Show that for a >=1,f(x)=sqrt(3)sinx-cosx-2a x+b is decreasing on Rdot

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

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  16. If a , b , c are real numbers, then find the intervals in which f(x)=|...

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  17. Find the intervals in which f(x)=(x-1)^3(x-2)^2 is increasing or decre...

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  18. Find the intervals in which f(x)=(4x^2+1)/x is increasing or decreasin...

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

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  20. Find the intervals for which f(x)=x^4-2x^2 increasing or decreasing.

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