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if f(x) ={{:( x,"for " xge 0),( -x ,"fo...

if f(x) ` ={{:( x,"for " xge 0),( -x ,"for " xlt 0 ):}then `

A

f(x) is continuous at x =0 but not differentiable

B

f(x) is continuous and differentiable at x=0

C

f(x) is differentiable at x=0

D

f(x) is not continuous at x=0

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The correct Answer is:
A
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NIKITA PUBLICATION-DIFFERENTIATION -MCQ
  1. Which of the following is not true

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  2. Which of the following is not true always ?

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  3. if f(x) ={{:( x,"for " xge 0),( -x ,"for " xlt 0 ):}then

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  4. If f(x) {{:( x,"for " xge 0),( -x ,"for " xlt 0 ):}then f(x) at x=0 ...

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  5. It f(x) = {{:((x^(2))/(|x|) ,"for " x ne 0 ),( 0, "for " x =0 ):}then

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  6. If f(x) = {{:( 1+ x ,"for " xle 2),( 5-x,"for " xgt 2):},then

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  7. If f(x) ={{:( x-1,"for " xlt2 ),( 2x-3 ,"for " xge 2 ):},then at x=2

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  8. If f (x) = {{:( x,"for" 0le xle 1 ),( 2x -1 ,"for " 1 lt x ):} then

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  9. If f(x) = {{:( x+ 2 , "for " -2 lt xlt3 ),(5,"for " x=3 ),( 8- x,for ...

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  10. If f(x) = {{:( 1-2x +3x^(2) -4x^(3) +......infty,"for" xne 1),( 1,"f...

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  11. The set of points where f(x)=x/(1+|x|) is differentiable is

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  12. If f(x) =|x-1| ,x in R then at x =1

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  13. If f(x)=x -|x| is

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  14. If f (x) =|x-1| +|x-2| ,then at x=2

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  15. If f (x) = {{:( xcos ((1)/(x)) ,"for " xne 0),( 0,"for " x=0) :},then...

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  16. IF f(x) = {{:( (1)/(2) sin ^(2) x , "for " x ne 0 ),( 0,"for " x=0 ):...

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  17. If f(x) {{:( 1,"for " (-pi)/( 2)lt x lt 0 ),( 1+sin x,"for" 0le xlt (...

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  18. If f(x) =[x] ,where x is the greatest integer not greater than x,-2 l...

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  19. If f(x) is derivable at x =2, where f(x) ={{:( x^(2),"for" xle 2 ),( ...

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  20. If the function g(x)={{:(,k sqrt(x+1),0 le x le3),(,mx+2,3lt xle5):...

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