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If f(x)= x^(2) sin ((1)/(x)), where x ne...

If `f(x)= x^(2) sin ((1)/(x))`, where `x ne 0`, then the value of the function f at x=0, so that the function is continuous at x= 0, is

A

0

B

`-1`

C

1

D

None of these

Text Solution

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The correct Answer is:
A
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-NCERT Exemplar Problems and Solution (Objective Type Questions)
  1. The function f(x)= cot x is discontinuous on the set

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  2. The function f(x)= e^(|x|) is

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  3. If f(x)= x^(2) sin ((1)/(x)), where x ne 0, then the value of the func...

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  4. If f(x) {(mx + 1,x le (pi)/(2)),((sin x)+ n,x gt (pi)/(2)):} is contin...

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  5. If f(x)= |sin x|, then

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  6. If y= log ((1- x^(2))/(1+ x^(2))), then (dy)/(dx) is equal to

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  7. If y= sqrt(sin x + y), then (dy)/(dx) is equal to

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  8. The derivative of cos^(-1) (2x^(2)-1) w.r.t cos^(-1)x is

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  9. If x= t^(2) and y= t^(3), then (d^(2)y)/(dx^(2)) is equal to

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  10. The value of c in Rolle's theorem for the function f(x)= x^(3) in the ...

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  11. For the function f(x)= x + (1)/(x), x in [1, 3] the value of c for mea...

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  12. If f(x)= 2x and g(x) = (x^(2))/(2) + 1, then which of the following ca...

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  13. The function f(x)= (4-x^(2))/(4x-x^(3)) is

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  14. The set of points where the function f given by f(x)= |2x-1| sin x is ...

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  15. The function f(x)= cot x is discontinuous on the set

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  16. The function f(x)= e^(|x|) is

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  17. If f(x)= x^(2) sin ((1)/(x)), where x ne 0, then the value of the func...

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  18. If f(x) {(mx + 1,x le (pi)/(2)),((sin x)+ n,x gt (pi)/(2)):} is contin...

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  19. If f(x) = |cos x|, then f'((pi)/(4)) is equal to …… 0 lt x lt (pi)/(2)

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  20. If y= log ((1- x^(2))/(1+ x^(2))), then (dy)/(dx) is equal to

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