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

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

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To solve the inequality \(\frac{x^2 - 4x + 7}{x^2 - 7x + 12} \leq \frac{2}{3}\), we will follow these steps: ### Step 1: Rearrange the inequality We start by moving \(\frac{2}{3}\) to the left side of the inequality: \[ \frac{x^2 - 4x + 7}{x^2 - 7x + 12} - \frac{2}{3} \leq 0 \] ...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Solve: (x^2-2x+5)/(3x^2-2x-5)>1/2 .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Without using the derivative show that the function f(x)=7x-3 is stric...

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

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