Q. 905.0( 1 Vote )

# Let f(x) = |sinx|. ThenA. f is everywhere differentiableB. f is everywhere continuous but not differentiable C. f is everywhere continuous but not differentiable at x = (2n + 1) D. None of these

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Super 10 Question: Check Your Knowledge of Maxima & Minima (Quiz)45 mins  Connection B/w Continuity & Differentiability59 mins  Maxima & Minima in an interval60 mins  Questions Based on Maxima & Minima57 mins  Check your Knowlege of Maxima & Minima ( Challenging Quiz)60 mins  Questions based on Maxima & Minima in an interval59 mins  Problems Based on L-Hospital Rule (Quiz)0 mins  When does a Maxima or Minima occur?48 mins  Interactive Quiz | Differentiability by using first principleFREE Class  Interactive Quiz on Limits67 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 