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

If `f(x) = |sinx|`, then

A

f is everywhere differentiable

B

f is everywhere continuous but not differentiable at `x = npi, n in Z`

C

f is ever ywhere continuous but not differentiable at `x = (2n+1)'(pi)/(2), n in Z`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `u(x)` and `v(x)` are both continuous.
Hence, `f(x) = vou(x)` is also a continuous function but `v(x)` is not differentiable at `x = 0`.
So, `f(x)` is not differentiable where `sinx = 0 rArr x = n pi, n in Z`
Hence, `f(x)` is continuous everywhere but not differentiable at `x = npi, n in Z`.
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NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
  1. The function f(x) = e^(|x|) is

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

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  3. If f(x)=[{:(mx+1,if x le (pi)/(2)),(sinx+n,ifxgt(pi)/(2)):} is contin...

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

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

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  6. If y = sqrt(sinx+y), then (dy)/(dx) is equal to

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

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

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

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

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

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

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

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

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

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

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

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  19. Trigonometric and inverse trigonometric functions are differentiable ...

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  20. If f.g is continuous at x = 0 , then f and g are separately continuou...

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