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  • The function <img alt="f\left ( x \right )= \left | \sin 4x \right |+\left | \cos 2x \right |" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cdpi%7B100%7D%20f%5Cleft%20%28%20x%20%5Cright%20

The function f\left ( x \right )= \left | \sin 4x \right |+\left | \cos 2x \right |,is a periodic function with period :

Option: 1

2\pi


Option: 2

\pi


Option: 3

\frac{\pi }{2}


Option: 4

\frac{\pi }{4}


Answers (1)

best_answer

As we have learnt,

  • If period of f(x) is T, then period of f(cx+d) is T/|c|
  • If period of f(x) is T1 and period of g(x) is T2, then period for f(x) + g(x) is the lcm of T1 and T2 
  • Period of |sin(x)| and |cos(x)| is π

 

Now, 

As period of |sin(x)| is π, so  period of |sin(4x)| is π/4, and

As period of |cos(x)| is π,  period of |cos(2x)| is π/2

So period of |sin(4x)| +  |cos(2x)| is the lcm of π/4 and π/2, which is π/2

 

 

Posted by

Deependra Verma

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