Então precisamos resolver:
underset(x -> - 1)(l i m) 2 x ³ + 7 x - 1
³
Pelo Teorema de Limite 4:
Se underset(x -> a)(lim) f ( x ) = L e underset(x -> a)(lim) g ( x ) = M , e n t ã o underset(x -> a)(lim) f (x) ∓ g ( x ) = L ∓ M
ã
underset(x -> - 1)(l i m) 2 x ³ + 7 x - 1 = underset(x -> - 1)(l i m) 2 x^3 + underset(x -> - 1)(l i m) 7 x - 1
³
Usando o Teorema de Limite 6:
Se underset(x -> a)(lim) f ( x ) = L e underset(x -> a)(lim) g ( x ) = M , e n t ã o underset(x -> a)(lim) f (x) . g ( x ) = L . M
ã
underset(x -> - 1)(l i m) 2 . underset(x -> - 1)(l i m) x^3 + underset(x -> - 1)(l i m) 7 x - 1
Pelo Teorema 1:
underset(x -> a)(lim) m x - b = m a - b
underset(x -> - 1)(l i m) 7 x - 1 = 7 (- 1) - 1 = - 8
Pelo Teorema 2:
underset(x -> - 1)(l i m) 2 = 2
Usando o Teorema 8:
Se underset(x -> a)(lim) f ( x ) = a , e n t ã o underset(x -> a)(lim) f (x)^n = a^n
ã
underset(x -> - 1)(l i m) x = - 1
underset(x -> - 1)(l i m) x ² = (- 1)^3 = - 1
²
Então:
underset(x -> - 1)(l i m) 2 . underset(x -> - 1)(l i m) x^3 + underset(x -> - 1)(l i m) 7 x - 1 = 2 . (- 1) - 8 = - 10