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y =
x
(x-3)(x+2)
lets try for the limit
lim
x -2
lim
x -2
=
-2
(-5)(+ε)
= (+)
(-)
(-)(+)
= +
f(x) =
x
x + 1
2
2
Find horizontal asymptotes (when x → +Ꝏ)
x
x + 1
2
2
make a modified function g(x). this is f(x) but the numerator and denominator are divided by the numerator
x
2
2
x
2
x
=
1
1 +
2
x
1
lim
x Ꝏ
=
1
1 + 0
g(x)
g(x) =
1
=
Vertical Asymptotes
Occurs when the limit is ±∞
Finding Limits at Infinity
For any function f(x) that has multiple terms with varying degrees of x, there exists insignificant terms
insignificant terms
For example:
x + x + 1
2
These terms are not the at highest degree, they are considered insignificant
Thus, when evaluating a limit at infinity, you can cancel these terms out
lim
x → ∞
= x + 0 + 0
2
= ∞