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Nilai lim_(x→2)⁡ ((x^2-5x-6) sin⁡ 2(x-2))/((x^2-x-2))=⋯

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Nilai limx→2(x2−5x−6)sin2(x−2)(x2−x−2)=⋯

  1. -8
  2. -5
  3. -2
  4. 3/4
  5. 5

(UM STIS 2017)

Pembahasan:

limx→2(x2−5x−6)sin2(x−2)(x2−x−2)=limx→2(x+1)(x−6)sin2(x−2)(x+1)(x−2)=limx→2(x−6)sin2(x−2)(x−2)=limx→2(x−6)⋅limx→2sin2(x−2)(x−2)=(2−6)⋅2=−8

Jawaban A.