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IME 508 - CDI I T12 (2015-1) UFRRJ - UNIVERSIDADE ESTADUAL DO RIO DE JANEIRO IME - INSTITUTO DE MATEMA´TICA E ESTATI´STICA ANMAT - DEPARTAMENTO DE ANA´LISE MATEMA´TICA Prof.a Cristiane Oliveira de Faria LISTA 1 DE CA´LCULO DIFERENCIAL E INTEGRAL I Revisa˜o: inequac¸o˜es, raizes e mo´dulos 1. Escreva usando a notac¸a˜o cient´ıfica: (a) 100.000.000 (c) (0, 00000009)2 (e) 2× 1016 − 0, 3× 1015 (b) 0, 0000021× 8.000 (d) √0, 00000002× 0, 0002 (f) ( 1.600× 20.000 4.000 )1/3 2. Simplifique: (a) (62)3/4 × 2−1/2 33/2 (b) ( √ 2)7/2 × 4√2 21−pi (c) 3 √ 3 × 62− √ 3 21− √ 3 (d) 22x × 10x 20x (e) (2pi)1−x × 4x pi × 2x−4 (f) x2(x+1) (2x)x + x2x 3. Resolva as inequac¸o˜es: (a) 3− 4x ≥ x+ 2 (b) 2x2 − x− 10 > 0 (c) −3x2 + 7x− 6 > 0 (d) x2 + x < x3 + 1 (e) 2x− 1 1− x ≤ 0 (f) x 2x− 3 ≤ 3 (g) x+ 1 x ≥ 2 (h) 1 x− 2 ≥ 5 2x− 1 (i) x+ 2 2− x < x2 − 4 2x− 1 4. Resolva para x e represente a soluc¸a˜o na reta nume´rica (a) |x− 3| = 6 (b) |3x− 1| = |x− 5| (c) |2x+ 3| = 2x+ 3 (d) |3 + 2x| ≤ 2 (e) |2x+ 5| > 3 (f) |3− 4x| > x+ 2 (g) x+ 1 |x2 − 1| ≥ x− 1 x− 1 (h) x+ 1 |x| + 1 |x2 − x| ≥ |x| 3 RESPOSTAS 1.(a) 108 (b) 168× 10−4 (c) 81× 10−16 (d) 2× 10−6 (e) 19, 7× 1015 (f) 20 2.(a) 2 (b) 21+pi (c) 18 (d) 2x (e) 25 × pi−x (f) x x+2 2x + xx 3.(a) (−∞, 1/5] (b) (−∞,−2) ∪ (5/2,∞) (c) ∅ (d) (−1, 1) ∪ (1,∞) (e) (−∞, 1/2] ∪ (1,∞) (f) (−∞, 3/2) ∪ [5/3,∞) (g) (0,∞) (h)(−∞, 1/2) ∪ (2, 3] (i) [−2, 1−√6] ∪ (1/2, 2) ∪ [1 +√6,∞) 4.(a) {−3, 9} (b) {−2, 3/2} (c) x ≥ −3/2 (d) [−5/2,−1/2] (e) (−∞,−4) ∪ (−1,∞) (f) (−∞, 1/5) ∪ (5/3,∞) (g)(−∞,−1) ∪ (−1, 0] ∪ (1, 2] (h)[−1.1, 0) ∪ (0, 1] ∪ (1, 4]
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