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Show that f(x)=tan^(-1)x-x is decreasing...

Show that `f(x)=tan^(-1)x-x` is decreasing function on `Rdot`

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RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTION -All Questions
  1. State when a function f(x) is said to be increasing on an interval [a ...

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  2. Determine whether f(x)=-x//2+sinx is increasing or decreasing on (-pi/...

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  3. Show that f(x)=tan^(-1)x-x is decreasing function on Rdot

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  4. Find the intervals in which f(x)=(x+2)e^(-x) is increasing or decreas...

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  5. Prove that the function f given by f(x)=x-[x] us increasing in (0,1)do...

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  6. Show that the function f given by f(x)=10^x is increasing for all xdot

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  7. Without using the derivative, show that the function f(x)=|x| is stric...

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

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  9. Prove that the function f(x)=(log)a x is increasing on (0,oo) if a &...

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

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

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

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  13. Show that f(x)=1/x is decreasing function on (0,oo)dot

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

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

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  16. Find dy/dx if x^2=siny

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

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

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

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

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