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Show that f(x)=logsinx is increasing on ...

Show that `f(x)=logsinx` is increasing on `(0,\ pi//2)` and decreasing on `(pi//2,\ pi)` .

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`f(x)=log(sinx)`
Diff. w.r.t. t, `f ′ (x)= 1/(sinx) ​ ×cosx=cotx` ...
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RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Show that f(x)=(log)a x ,\ \ 0<a<1 is a decreasing function for all ...

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  2. Show that f(x)=sinx is increasing on (0,\ pi//2) and decreasing on (pi...

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  3. Show that f(x)=logsinx is increasing on (0,\ pi//2) and decreasing on ...

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  4. Show that f(x)=x-sinx is increasing for all x in R .

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  5. Show that f(x)=x^3-15 x^2+75 x-50 is an increasing function for all...

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  6. Show that f(x)=cos^2x is a decreasing function on (0,\ pi//2) .

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  7. Show that f(x)=sinx is an increasing function on (-pi//2,\ pi//2) .

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  8. Show that f(x)=cosx is a decreasing function on (0,\ pi) , increasing ...

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  9. Show that f(x)=tanx is an increasing function on (-pi//2,\ pi//2) .

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  10. Show that f(x)=tan^(-1)(sinx+cosx) is a decreasing function on the ...

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

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

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

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

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

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

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

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

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

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  20. Determine whether f(x)=-x/2+sinx is increasing or decreasing on (-pi/3...

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