lim_(x→1) (sin(x−1))/(x^(2)−3x+2)=⋯ a. 0 d. −1 b. −1/2 e. 1 c. 1/2

Jawaban yang benar adalah d. -1 Ingat limit trigonometri : lim_(x→0) (sin x)/(x) = 1 Pembahasan : lim_(x→1) (sin(x−1))/(x²−3x+2) = lim_(x→1) (sin(x−1))/((x–2)(x–1)) Misalkan : y = x – 1 y + 1 = x Karena x → 1 maka y → 0 lim_(x→1) (sin(x−1))/((x–2)(x–1)) = lim_(y→0) (sin y)/(((y+1)–2)y) = lim_(y→0) (sin y)/((y+1–2)y) = lim_(y→0) (sin y)/((y–1)y) = lim_(y→0) (sin y)/(y) · 1/(y–1) = 1 · 1/(0-1) = 1 · 1/(-1) = 1/(-1) = -1 Jadi nilai dari lim_(x→1) (sin(x−1))/(x²−3x+2) = -1 Oleh karena itu jawaban yang benar adalah D