No. of real solutions of : cosx = |x|
Answer (1)
22nd Dec, 2019
Hello,
The given eqn is,
cos x = l x l
If graph is drawn for y =x and y = cos x, then the graph will intersect at exactly one point ( 0.5 , 1 )
So, the number of real solutions for cos x = l x l is one.
The solution for above eqn will range from 0.5 to 1.
Let,
f(x)=x−cosx
Then:
f'(x)=1+sinx
By Newton Raphson's Method:
ai+1=ai − [ f(ai) / f'(ai) ]
By solving the above eqn by iterative method by using Newton Raphson's method, we find the approximate value of x = 0.739
So, the solution of given eqn is 0.739
Best Wishes.
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