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Let f o^n (f(x)) denote the composition of f(x) with itself n number of times then the value of ltn → ∞ f o^n (sin(x)) =

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Let  f o^n (f(x)) denote the composition of  f(x) with itself n number of times then the value of   ltn → ∞  f o^n (sin(x)) =

(a) -1

(b) 2

(c) ∞

(d) 0

I had been asked this question in quiz.

Question is taken from Indeterminate Forms in portion Differential Calculus of Engineering Mathematics

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Right answer is (d) 0

The best I can explain: Drawing the graph of y = x and y = sin(x)  we can write the limit value as 0.

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