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If f(x) = x^(2)sin'(1)/(x), where x ne 0...

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 the above

Text Solution

Verified by Experts

The correct Answer is:
A
`:. f(x) = x^(2)sin(1/x)`, where `x ne 0`
Hence, value of the function f at x = 0, so that it is continuous at `x = 0` is 0.
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NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
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  2. The function f(x) = e^(|x|) is

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

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  7. If y = sqrt(sinx+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) 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) - 3...

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

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  12. An example of a function which is continuous every where but fails to...

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  13. Derivative of x^(2) w.r.t. x^(3) is "……."

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  14. If f(x) = |cosx|, then f'(pi/4) is equal to "……."

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  15. For the curve sqrt(x) + sqrt(y) = 1, (dy)/(dx) at (1/4,1/4) is "……….".

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  16. Rolle's theorem is applicable for the function f(x) = |x-1| in [0,2].

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  17. If f is continuous on its domain D; then |f| is also continuous on D

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  18. If f is continuous on its domain D; then |f| is also continuous on D

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  19. The composition of two continuous function is a continuous function.

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