Question

Use mean value theorem to prove |sin x- sin y |<= x-y for all x,y in R

Answer 1

Answer:

mean value theorem to prove the inequality |sinx−siny|≤|x−y| for all x,y∈R?

So let us set f(x)=sinx then it's differentiable on (x,y) and continuous on [x,y]. So there exists c on (x,y) such that f′(c)=sinx−sinyx−y.

Since max(sinx−siny) is 2 where |x−y|=π≥2. So I guess then we make the conclusion.

Step-by-step explanation:

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