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Show that the function f(x)=cot^(-1)(sin...

Show that the function `f(x)=cot^(-1)(sinx+cosx)` is decreasing on `(0,\ pi//4)` and increasing on `(pi//4,\ pi//2)` .

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

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  2. Show that the function f(x)=sin(2x+pi//4) is decreasing on (3pi//8,\ 5...

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  3. Show that the function f(x)=cot^(-1)(sinx+cosx) is decreasing on (0,\ ...

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  4. Show that f(x)=(x-1)e^x+1 is an increasing function for all x >0 .

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  5. Show that the function x^2-x+1 is neither increasing nor decreasing...

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  6. Show that f(x)=x^9+4x^7+11 is an increasing function for all x in ...

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  7. Prove that the function f(x)=x^3-6x^2+12 x-18 is increasing on R .

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  8. State when a function f(x) is said to be increasing on an interval ...

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  9. Show that f(x)=sinx-cosx is an increasing function on (-pi//4,\ pi//4)...

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

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

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  12. Find the intervals in which f(x)=log(1+x)-x/(1+x) is increasing or dec...

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

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

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  15. Prove that the function f given by f(x)=x-[x] is increasing in (0,\ 1)...

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  16. Prove that the function f(x)=3x^5+40 x^3+240 x is increasing on R .

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  17. Prove that the function f given by f(x)=logcosx is strictly increasing...

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  18. Show that the function f given by f(x)=x^3-3x^2+4x ,x in Ris strictl...

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  19. Prove that the function f(x)=cosx is strictly decreasing in (0,\ pi)

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  20. Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

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