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

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

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To solve the inequality \(\frac{x^2 - 2x + 5}{3x^2 - 2x - 5} > \frac{1}{2}\), we will follow these steps: ### Step 1: Rewrite the Inequality Start by rewriting the inequality: \[ \frac{x^2 - 2x + 5}{3x^2 - 2x - 5} - \frac{1}{2} > 0 \] ...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
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  2. Sol v e(8x^2+16 x-51)/(2x^2+5x-12)>3

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Show that f(x)=1/(1+x^2) is neither increasing nor decreasing on R ...

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  20. Without using the derivative, show that the function f(x)=|x| is (a) s...

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