1. Mostrar que existe o limite de f(x) = 4x - 5 em x = 3 e q...

1. Mostrar que existe o limite de f(x) = 4x - 5 em x = 3 e que é igual a 7.
2. Mostrar que lim[x->3] x^2 = 9 Calcule os seguintes limites usando as propriedades dos limites:

(a) lim[x->0](3 - 7x - 5x^2) (b) lim[x->-1](-x^5 + 6x^4 + 2) (c) lim[x->1]((x + 4)^3 . (x + 2) - 1) (d) lim[x->2] x + 4 (e) lim[x->1] 3x - 1 (f) lim[t->2] t^2 - 5t + 6 (g) lim[x->4] 3√(2x + 3) (h) lim[x->√2] 2x^2 - x / 3x (i) lim[x->π/2][2 . sen x - cos x + cotg x]

3. Dadas as integrais abaixo, calcule cada uma delas:

(a) ∫[0 to 4] (3x^2 - 2x + 1) dx (b) ∫[0 to ∞] 1/√(x + 1) dx (c) ∫[0 to 3] e^x dx (d) ∫[0 to 2] x ln(x) dx (e) ∫[1 to ∞] 1/x^2 dx (f) ∫[0 to ∞] e^(-x) dx (g) ∫[0 to 1] 1/√(1 - x^2) dx (h) ∫[0 to 2] xe^(x^2) dx (i) ∫[0 to 1] x cos(x) dx (j) ∫[0 to ∞] sin(x)/x dx (k) ∫[0 to ∞] sin(x) dx (l) ∫[0 to ∞] e^(-x) dx (m) ∫[1 to 4] 2x/(x^2 + 1) dx (n) ∫[0 to π/2] e^(x) sin(x) dx (o) ∫[0 to π/2] tan(x) dx (p) ∫[1 to ∞] 1/x dx (q) ∫[0 to 1] 1/(1 - x^2)^2 dx (r) ∫[0 to π] cos^2(x) dx (s) ∫[0 to 1] 1/√(1 - x^2) dx (t) ∫[1 to 2] ln(x) dx