MAT1613
ASSIGNMENT 1
2023
, Solution:
a).
1 − 2x 2
f(x) =
x2 − 1
Vertical astmptotes ∶ x 2 − 1 = 0
x2 − 1 = 0
(x − 1)(x + 1) = 0
x = 1 or x = −1
Vertical astmptotes: x = 1 and x = −1
Horizontal asymptotes:
1 − 2x 2
lim f(x) = lim
x→∞ x→∞ x 2 − 1
1
x 2 ( 2 − 2)
= lim x
x→∞ 2 1
x (1 − 2 )
x
ASSIGNMENT 1
2023
, Solution:
a).
1 − 2x 2
f(x) =
x2 − 1
Vertical astmptotes ∶ x 2 − 1 = 0
x2 − 1 = 0
(x − 1)(x + 1) = 0
x = 1 or x = −1
Vertical astmptotes: x = 1 and x = −1
Horizontal asymptotes:
1 − 2x 2
lim f(x) = lim
x→∞ x→∞ x 2 − 1
1
x 2 ( 2 − 2)
= lim x
x→∞ 2 1
x (1 − 2 )
x
