Nilai limx→1 (x2+x−2)sin(x2−1)x2−2x+1=⋯
- −4
- −34
- 12
- 3
- 6
(UM UNDIP 2011)
Pembahasan:
limx→1 (x2+x−2)sin(x2−1)x2−2x+1=limx→1 (x+2)(x−1)sin(x+1)(x−1)(x−1)(x−1)=limx→1 (x+2)sin(x+1)(x−1)(x−1)=limx→1 (x+2)⋅limx→1 sin((x+1)(x−1))(x−1)=limx→1(x+2)⋅(x+1)=(1+2)(1+1)=3⋅2=6
Jawaban E.