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Question

Show that the function given by f(x) = sin x is

(a) strictly increasing in (b) strictly decreasing in

(c) neither increasing nor decreasing in (0, π)

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Solution

The given function is f(x) = sin x.

(a) Since for eachwe have.

Hence, f is strictly increasing in.

(b) Since for each, we have.

Hence, f is strictly decreasing in.

(c) From the results obtained in (a) and (b), it is clear that f is neither increasing nor decreasing in (0, π).


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