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If f (x) = {{:( x,"for" 0le xle 1 ),( 2...

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

A

f(x) is discontinuous at x=1

B

f (x) is differntiable at x=1

C

f(x) is continuous but not differentiable at x=1

D

f (x) is not continuous but differentiable at x=1

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The correct Answer is:
C
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NIKITA PUBLICATION-DIFFERENTIATION -MCQ
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  2. If f(x) ={{:( x-1,"for " xlt2 ),( 2x-3 ,"for " xge 2 ):},then at x=2

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. The value of m which the function f(x) {{:( mx^(2), "for " xle 1 ),( ...

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  17. If f (x) ={{:( px^(2) +q,"for " xle 1),( qx^(2) +px +r ,"for " xlgt 1...

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  18. Let f(x)={{:(,x^(n)"sin "(1)/(x),x ne 0),(,0,x=0):} Then f(x) is conti...

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  19. If f(x) = {{:( e^(x) +ax ,"for " x lt 0 ),( b(x-1) ^(2) ,"for " xge 0...

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  20. If f (x)= ae^(|x|)+b |x|^(2) ,a ,b in R and f(x) is differentiable...

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