Resolva as inequações abaixo: (a) |2x− 5| 2x + 1/(x + 1) (s) 1/(x− 1) − 1/(2x + 1) > −3 (t) |x^2 − x| > 2

(a) |2x-5| -1 2x 4 x 2 (b) |3x+5| ≤ |2x+1| 3x+5 ≤ 2x+1 e 3x+5 ≥ -(2x+1) x ≤ -2 e x ≥ -2/5 (c) |x-2| ≥ |4x+1| x-2 ≤ -(4x+1) ou x-2 ≥ 4x+1 x ≤ -1 ou x ≥ 3/5 (d) x² ≤ 4 -2 ≤ x ≤ 2 (e) 3 4 (i) 5/3-x ≥ 2 x ≥ -1/2 (j) (x+2)/(x-1) ≤ x/(x+4) x²+2x ≤ x²+3x-4 x ≥ -4 (k) x³-x+1/2 1/2 (p) -6 ≤ x²-5x 2x+1/(x+1) x 1/2 (s) 1/(x-1)-1/(2x+1) > -3 x 1/2 (t) |x²-x| > 2 x 2

Resolva as inequações abaixo: (a) |2x− 5| < 1 (b) |3x + 5| ≤ |2x + 1| (c) |x− 2| ≥ |4x + 1| (d) x2 ≤ 4 (e) 3 < 5x ≤ 2x + 11 (f) 2x ≥ 3x2 − 16 (g)...

Resolva as inequações abaixo: (a) |2x− 5| < 1 (b) |3x + 5| ≤ |2x + 1| (c) |x− 2| ≥ |4x + 1| (d) x2 ≤ 4 (e) 3 < 5x ≤ 2x + 11 (f) 2x ≥ 3x2 − 16 (g) 0 < x− 1/2x− 1 < 2 (h) 2/x − 4 < 3/x − 8 (i) 5/(3− x) ≥ 2 (j) (x + 2)/(x− 1) ≤ x/(x + 4) (k) x^3 − x + 1/2 < 1− x/4 (l) (x− 1)(2x− 3) ≥ 0 (m) (x− 2)(−2x− 4)(x− 4) ≤ 0 (n) 3x/(x + 1) + 5/2 ≤ 7/(2x + 2) (o) 5/(2x− 1)^2 ≥ 7/x (p) −6 ≤ x^2 − 5x < 6 (q) (x^2 + 2x− 3)(3x^2 − 4x + 8) < 0 (r) (x− 1)/(x + 2) > 2x + 1/(x + 1) (s) 1/(x− 1) − 1/(2x + 1) > −3 (t) |x^2 − x| > 2

Cálculo I

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Lista de Exercícios de Cálculo I

Cálculo I • Fundação Universidade Federal de ViçosaFundação Universidade Federal de Viçosa

Gustavo Daniel da Cunha

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Ed

18.01.2024

(a) |2x-5| < 1 2x-5 < 1 e 2x-5 > -1 2x < 6 e 2x > 4 x < 3 e x > 2 (b) |3x+5| ≤ |2x+1| 3x+5 ≤ 2x+1 e 3x+5 ≥ -(2x+1) x ≤ -2 e x ≥ -2/5 (c) |x-2| ≥ |4x+1| x-2 ≤ -(4x+1) ou x-2 ≥ 4x+1 x ≤ -1 ou x ≥ 3/5 (d) x² ≤ 4 -2 ≤ x ≤ 2 (e) 3 < 5x ≤ 2x+11 3/5 < x ≤ 3 (f) 2x ≥ 3x²-16 3x²-2x-16 ≤ 0 x ≤ (-(-2) - √((-2)²-4(3)(-16)))/(2(3)) ou x ≥ (-(-2) + √((-2)²-4(3)(-16)))/(2(3)) x ≤ -2 ou x ≥ 8/3 (g) 0 < x-1/2x-1 < 2 1/2 < x < 3 (h) 2/x-4 < 3/x-8 x < 2 ou x > 4 (i) 5/3-x ≥ 2 x ≥ -1/2 (j) (x+2)/(x-1) ≤ x/(x+4) x²+2x ≤ x²+3x-4 x ≥ -4 (k) x³-x+1/2 < 1-x/4 x³+3x/4 < 1 (l) (x-1)(2x-3) ≥ 0 x ≤ 1/2 ou x ≥ 3/2 (m) (x-2)(-2x-4)(x-4) ≤ 0 -4 ≤ x ≤ -2 ou 2 ≤ x ≤ 4 (n) 3x/(x+1)+5/2 ≤ 7/(2x+2) x ≤ -1 ou x ≥ 1/2 (o) 5/(2x-1)² ≥ 7/x x > 1/2 (p) -6 ≤ x²-5x < 6 1 ≤ x ≤ 4 ou x < -1 (q) (x²+2x-3)(3x²-4x+8) < 0 -2-√7 < x < -1 ou 1 < x < √3-1 (r) (x-1)/(x+2) > 2x+1/(x+1) x < -2 ou x > 1/2 (s) 1/(x-1)-1/(2x+1) > -3 x < -1 ou x > 1/2 (t) |x²-x| > 2 x < -1 ou x > 2

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