Tugas 1 Kalkulus (MATA4110) PDF

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TUGAS 1 KALKULUS (MATA4110)

Nama : Nurul Rahmadhani NIM : 04099447 Program Studi : Teknologi Pangan

FAKULTAS SAINS DAN TEKNOLOGI UNIVERSITAS TERBUKA 2022

1. Diketahui A = {x ∣ x2 – 1 = 0 }, B = {x ∣ x2 + x – 2 = 0 }, C = {x ∣ x3 – x2 = 0 } A,B,C ⸦ R Tentukan : A. A ∪ (𝐵 ∩ 𝐶) B. (A ∪ 𝐵) ∩ 𝐶 C. (A – B ) ∪ 𝐶 Jawab: A= {x ∣ x2 – 1 = 0 }= (x + 1)(x-1) = 0, x1= -1,x2= 1, sehingga A={-1, 1} B = {x ∣ x2 + x – 2 = 0 }= (x – 1) (x+2), x1= 1, x2 = -2, sehingga B={-2,1} C = {x ∣x3 – x2 = 0 }= (x2) (x – 1) = 0 , x1=0, x2=1, sehingga C={0,1} Maka, A. A ∪ (𝐵 ∩ 𝐶) = {-1, 1} ∪ ( −2, 1 ∩ 0,1 ) = {-1,1} ∪ 1 = {−1,1} B. (A ∪ 𝐵) ∩ 𝐶 = ({-1,1} ∪ {−2,1}) ∩ {0,1} = {−2, −1, 1} ∩ {0,1} = {1}

C. (A – B ) ∪ 𝐶 = ({-1, 1} – {-2,1}) ∪ 0,1 = −1 ∪ 0,1 = {−1, 0 ,1} 2. Tentukan himpunan penyelesaian: a) – 5 ≤ 2𝑥 − 5 < 5  – 5 ≤ 2𝑥 − 5 < 5 -5 +5 ≤ 2𝑥 − 5 + 5 < 5 + 5 0 ≤ 2𝑥 < 10 0 ≤x...