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Prove that the function f(x)=(log)e x is...

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

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RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTION -All Questions
  1. Show that the function f(x)=x^2 is a strictly decreasing function on...

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

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

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  4. Find the second order derivative of the function f(x)=logx with respec...

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

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

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

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

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

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

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

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

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  13. Find the intervals in which the function f(x)=2x^3-9x^2+12 x+15 is inc...

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

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

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

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

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  18. Find the intervals in which the function f(x)=log(1+x)-(2x)/(2+x) is i...

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

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

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