MAT1613
ASSIGNMENT 1
2022
, QUESTION 1
Solution:
a).
𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑎𝑠𝑦𝑚𝑝𝑡𝑜𝑡𝑒𝑠:
𝑥2
𝑦 = lim
𝑥→∞ (−2𝑥 + 1)2
𝑥2
= lim
𝑥→∞ (−2𝑥 + 1)(−2𝑥 + 1)
𝑥2
= lim
𝑥→∞ 4𝑥 2 − 4𝑥 + 1
𝑥2
= lim
𝑥→∞ 2 4 1
𝑥 (4 − + 2 )
𝑥 𝑥
1
= lim
𝑥→∞ 4 1
(4 − 𝑥 + 2 )
𝑥
1
=
(4 − 0 + 0)
1
=
4
𝟏
𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝒂𝒔𝒚𝒎𝒑𝒕𝒐𝒕𝒆𝒔: 𝒚 =
𝟒
ASSIGNMENT 1
2022
, QUESTION 1
Solution:
a).
𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑎𝑠𝑦𝑚𝑝𝑡𝑜𝑡𝑒𝑠:
𝑥2
𝑦 = lim
𝑥→∞ (−2𝑥 + 1)2
𝑥2
= lim
𝑥→∞ (−2𝑥 + 1)(−2𝑥 + 1)
𝑥2
= lim
𝑥→∞ 4𝑥 2 − 4𝑥 + 1
𝑥2
= lim
𝑥→∞ 2 4 1
𝑥 (4 − + 2 )
𝑥 𝑥
1
= lim
𝑥→∞ 4 1
(4 − 𝑥 + 2 )
𝑥
1
=
(4 − 0 + 0)
1
=
4
𝟏
𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝒂𝒔𝒚𝒎𝒑𝒕𝒐𝒕𝒆𝒔: 𝒚 =
𝟒
