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If f(x)={((sin[x])/([x]), [x]!=0),(0,[x]...

If `f(x)={((sin[x])/([x]), [x]!=0),(0,[x]=0):}`
where [.] denotes the greatest integer less than or equal to x then

A

Continuous at x =0

B

Left continuous at x =0

C

Discontinuous at x =0

D

Right continuous at x = 0

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH INSTITUTE ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Assignment ( section -A)
  1. Let f(x) = (x(2^(x)-1))/( 1- cos x) for x ne 0 what choice of f(0)...

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  2. If f(x)={:{([x]+[-x] , xne 0), ( lambda , x =0):} where [.] denotes...

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  3. If f(x)={((sin[x])/([x]), [x]!=0),(0,[x]=0):} where [.] denotes the ...

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  4. Let f(x) = sin"" 1/x, x ne 0 Then f(x) can be continuous at x =0

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  5. If f(x) = {:{(px^(2)-q, x in [0,1)), ( x+1 , x in (1,2]):} and f(1...

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  6. let f(x) = {:{( x^(2) , x le 0) , ( ax , x gt 0):} then f (x) is d...

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  7. If f is derivable at x =a,then underset(xto a ) lim( (xf(a) -af( x))/...

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  8. Let f(x) = x|x| then f'(0) is equal to

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  9. If f(x) =|x| , then f'(0) is

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  10. Let f(x)= {:{ (x + a , x ge 1 ) , ( ax^(2) + 1, x lt 1) :} then f(x)...

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  11. If f(x )=sqrt(25-x^(2)), then what is underset(xto1)lim(f(x)-f(1))/(x-...

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  12. if f(x)=e^(-1/x^2),x!=0 and f (0)=0 then f'(0) is

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  13. If f(x)=log|x|,xne0 then f'(x) equals

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  14. d/(dx) (sin^(-1) "" (2x)/(1+x^(2))) is equal to

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  15. Differential coefficient of log10 x w.r.t logx 10 is

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  16. Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))^(3/4)}

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  17. If y=(e^x-e^(-x))/(e^x+e^(-1)),"p r o v et h a t"(dy)/(dx)=1-y^2

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  18. If y=ae^(mx)+be^(-mx) then (d^2y)/(dx^2) is

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  19. If y^(2) = ax^(2) + b , " then " (d^(2)y)/( dx^(2))

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  20. If y=(log x)/(x) then (d^(2)y)/(dx^(2))=

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