MAT1613
ASSIGNMENT 1
2024
, QUESTION 1
Solution:
a).
Horizontal asymptote:
y = lim f(x)
x→∞
x
y = lim
x→∞ (x − 1)2
x
y = lim
x→∞ x 2
− 2x + 1
x
y = lim
x→∞ 1
x (x − 2 + x )
1
y = lim
x→∞ 1
x−2+x
y=0
Vertical asymptote:
x
f(x) =
(x − 1)2
∴ (x − 1)2 = 0
x−1=0
ASSIGNMENT 1
2024
, QUESTION 1
Solution:
a).
Horizontal asymptote:
y = lim f(x)
x→∞
x
y = lim
x→∞ (x − 1)2
x
y = lim
x→∞ x 2
− 2x + 1
x
y = lim
x→∞ 1
x (x − 2 + x )
1
y = lim
x→∞ 1
x−2+x
y=0
Vertical asymptote:
x
f(x) =
(x − 1)2
∴ (x − 1)2 = 0
x−1=0
