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Solve: (1+x^2)/(x^2-5x-6)<0...

Solve: `(1+x^2)/(x^2-5x-6)<0`

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To solve the inequality \(\frac{1+x^2}{x^2-5x-6} < 0\), we will follow these steps: ### Step 1: Rewrite the Inequality We start with the given inequality: \[ \frac{1+x^2}{x^2-5x-6} < 0 \] ...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Solve: 4x^3-24 x^2+44 x-24 >0 .

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  2. Solve: 1/(x+1)-4/((2+x)^2)>0,\ \ x!=-1,\ -2 .

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  3. Solve: (1+x^2)/(x^2-5x-6)<0

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

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  5. Solve: (x^2-2x+5)/(3x^2-2x-5)>1/2 .

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  6. Solve: (x^2-2x+24)/(x^2-3x+4)lt=4 .

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  7. Solve: (x^2-4x+7)/(x^2-7x+12)lt=2/3 .

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  8. Show that the function f(x)=2x+3 is strictly increasing function on...

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  9. Show that the function f(x)=x^2 is strictly increasing function on ...

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  10. Show that the function f(x)=a^x ,\ a >1 is strictly increasing on Rdot

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  11. Show that the function f(x)=-3x+12 is strictly decreasing function ...

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  12. Show that the function f(x)=a^x ,\ 0<a<1 is strictly decreasing on R .

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  13. Show that the function f(x)=x^2 is a strictly decreasing function o...

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  14. Show that the function f(x)=x^2 is neither strictly increasing nor ...

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  15. Prove that the function f(x)=(log)e x is increasing on (0,\ oo) .

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  16. Prove that the function f(x)=(log)a x is increasing on (0,\ oo) if a >...

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  17. Prove that f(x)=a x+b , where a ,\ b are constants and a >0 is an incr...

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  18. Prove that f(x)=a x+b , where a ,\ b are constants and a<0 is a decrea...

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  19. Show that f(x)=1/x is a decreasing function on (0,\ oo) .

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  20. Show that f(x)=1/(1+x^2) decreases in the interval [0,\ oo) and increa...

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