nilai limit x menuju 2 2/x²-4 -3/x²+2x-8=... a. -7/12 b. -1/4 c. -1/12 d. -1/24 e. 0
Matematika
danuhadi95
Pertanyaan
nilai limit x menuju 2 2/x²-4 -3/x²+2x-8=...
a. -7/12
b. -1/4
c. -1/12
d. -1/24
e. 0
a. -7/12
b. -1/4
c. -1/12
d. -1/24
e. 0
1 Jawaban
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1. Jawaban arsetpopeye
Lim (2/(x^2 - 4) - 3/(x^2 + 2x - 8)
= Lim 2/(x + 2)(x - 2) - 3/(x + 4)(x - 2)
= Lim (2(x + 4) - 3(x + 2)) / (x + 2)(x - 2)(x + 4)
= Lim (2x + 8 - 3x - 6) / (x + 2)(x - 2)(x + 4)
= Lim (-x + 2) / (x + 2)(x - 2)(x + 4)
= Lim -1(x - 2) / (x + 2)(x - 2)(x + 4)
= Lim -1 / (x + 2)(x + 4)
= -1/(2 + 2)(2 + 4)
= -1/(4)(6)
= -1/24