Q. 905.0( 1 Vote )

Let f(x) = |sinx|. Then
A. f is everywhere differentiable

B. f is everywhere continuous but not differentiable

C. f is everywhere continuous but not differentiable at x = (2n + 1)

D. None of these

Answer :

Given that, f(x) = |sinx|


Let g(x) = sinx and h(x) = |x|


Then, f(x) = hog(x)


We know that, modulus function and sine function are continuous everywhere.


Since, composition of two continuous functions is a continuous function.


Hence, f(x) = hog(x) is continuous everywhere.


Now, v(x)=|x| is not differentiable at x=0.


Lv’(0) =


=


= ( v(x) = |x|)


=


=


=


Rv’(0) =


=


= ( v(x) = |x|)


=


=


=


Lv’ (0) ≠ Rv’(0)


|x| is not differentiable at x=0.


h(x) is not differentiable at x=0.


So, f(x) is not differentiable where sinx = 0


We know that sinx=0 at x = nπ, n Z


Hence, f(x) is everywhere continuous but not differentiable x = nπ, n Z

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