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Practice Problems 1 Solutions

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Practice Problems 1 Solutions

1. 1. Practice Problems 1: Solutions 1. V = A 1 1 150 1− 1− n ⇒ 437 = 3 r r (1 + r) (1 + r) (2x) 2. (a) lim (2x) x 0 (b) lim √ x→∞ r = 0.014802 =1 1 =0 4x2 − 2x − 10 + 2x 1 −1 = (5 − x) 5−x 3. (a) f (x) = f (x) = (−1) (5 − x) −2 (−1) = 1 where x = 5 2 (5 − x) 10 ke−ak x (b) f (x) = 2 k=1 10 10 2 k (−2ak x) e−ak x = −2 f (x) = k=1 log (c) f (x) = f (x) = (d) f (x) = x K 2 + r−q+ σ 2 √ σ T −t 1 σ T −t S K K x (T − t) 1 K 2 + r−q+ x 2 √ x T −t = 1 √ σx T − t (T − t) √ x T − t (x(T − t)) − log f (x) = S K S K − r−q− √ x2 T − t x2 2 x2 2 (T − t) √ T −t − t) (T − t) sin 3x2 6x cos 3x2 6 cos 3x2 − 36x2 sin 3x2 3 = lim = lim = 2 0 x 0 x 0 2x 4x 4 2 4. (a) lim x + r−q− x2 (T − log = 2 k=1 √ log kak xe−ak x 4x3/x4 log x4 4 = lim = lim =0 x→∞ x→∞ x→∞ x x 1 (b) lim