Question: (a) Use Exercise 55 to prove that | sin a sin b| |a b| for all a, b. (b) Let (x) =
(a) Use Exercise 55 to prove that | sin a − sin b| ≤ |a − b| for all a, b.
(b) Let (x) = sin(x + a) − sin x. Use part (a) to show that the graph of ƒ lies between the horizontal lines y = ±a.
(c) Plot y = ƒ(x) and the lines y = ±a to verify (b) for a = 0.5 and a = 0.2.
Data From Exercise 55
Use FTC I to prove that if |ƒ'(x)| ≤ K for x ∈ [a, b], then |ƒ'(x) − ƒ(a)| ≤ K|x − a| for x ∈ [a, b].
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a Let fx sin x so that fx cos x and for all x From Exercise 55 we get sin a si... View full answer
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