Question: proof it all Theorem 2.2. Let a be a constant. Then (a) Aa' = (a - 1)at. (b) A sin at = 2 sin &

proof it all

Theorem 2.2. Let a be a constant. Then (a) Aa' = (a - 1)at. (b) A sin at = 2 sin & cos a(t + 2). (c) A cosat = -2 sin ; sina(t + 5). (d) A logat = log(1 + =). (e) A log (t) = logt. (Here log t represents any logarithm of the positive number t.) Proof. We leave the verification of parts (a)-(d) as exercises. For part (e), A log (t) = log (t + 1) - log (t) r(t + 1) = log r(t) = log t (see Example 1.6)

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