Question

Soal:
[tex]\displaystyle\lim_{x\to - 2} \: \frac{ {x}^{2} + x - 6 }{ {x}^{2} + 9x + 18 }[/tex]
Hasilnya adalah...
a. -0
b. 0
c. -1
d. 1

#limit gampang​

Answer 1

Verified answer

[tex]\displaystyle\lim_{x\to - 2} \: \frac{ {x}^{2} + x - 6 }{ {x}^{2} + 9x + 18 }[/tex]

= x(x + 3) - 2(x + 3)/x(x + 6) + 3(x + 6)

= (x + 3)(x - 2)/(x + 6)(x + 3)

= (x + 3)/(x + 3)(x - 2)/(x + 6)

= (x - 2)/(x + 6)

= (-2 - 2)/(-2 + 6)

= -4/4

= -1

Answer 2

Jawaban:

Cara pemfaktoran:

lim x→(-2) (x² + x - 6)/(x² + 9x + 18)

lim x→(-2) (x+3)(x-2)/(x+3)(x+6)

eliminasi/coret persamaan (x+3), menghasilkan:

(x-2)/(x+6) → substitusi nilai x

(x-2)/(x+6) = (-2-2)/(-2+6) = -4/(4) = -1

Cara substitusi langsung:

lim x→(-2) (x² + x -6)/(x²+9x+18)

substitusi nilai x = -2 langsung:

(x²+x-6)/(x²+9x+18) = {(-2)²+(-2)-6}/{(-2)²+9(-2)+18} = {4-2-6}/{4-18+18} = -4/4 = –1

Opsi (C)