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f (x) =2x -tan ^(-1) x - ln (x+ sqrt(1+ ...

`f (x) =2x -tan ^(-1) x - ln (x+ sqrt(1+ x ^(2)))`

A

f (x) in non-increasing in `(-oo,oo)`

B

f (x) in non-decreasing in `(-oo,oo)`

C

f (x) is increasing in `(-oo,oo)`

D

None of these

Text Solution

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The correct Answer is:
B, C
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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS 2-Level -1
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  2. Discuss monotonocityt of y =f(x) which is given by x=(1)/(1+t^(2))and ...

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  3. f (x) =2x -tan ^(-1) x - ln (x+ sqrt(1+ x ^(2)))

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  4. Write the set of values of a for which f(x)=cosx+a^2\ x+b is strictly ...

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  5. Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreas...

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  6. Find the range of values of a if f(x)=2e^x-a e^(-x)+(2a+1)x-3 is monot...

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  7. If f (x)=a ln |x| +bx^(2) +x has extremas at x=1and x=3 then:

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  8. if f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)),(- cos x, -(pi)/(2)lt x ,le 0...

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  9. The function f(x)=(x^2-4)^n(x^2-x+1),n in N , assumes a local minimum...

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  10. The function f(x)=|x^2-2|/|x^2-4| has, (a) no point of local maxima ...

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  12. If xy =10, then minimum value of 12x^2 + 13y^2 is equal to :

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  13. If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

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  14. Let f(x)={:{(|x-2|+a^(2)-9a-9","ifxlt2),(2x-3"," if xge2):} Then, f...

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  15. Let f(x)={{:(,x^(3)+x^(2)-10x,-1 le x lt 0),(,cos x,0 le x lt pi/2),(,...

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  16. The third derivative of a function f'''(x) vanishes for all f(0)=1,f'(...

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  17. The least value of alpha in R for which 4ax^2+(1)/(x)ge1, for all xgt ...

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  18. The number of critical points of f(x)=max{sinx,cosx},AAx in(-2pi,2pi),...

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  19. Let f(x) = Maximum {sin x, cos x} AA x in R. minimum value of f (x) ...

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