Limit algebra - brief list
∞±L = ∞ for all real L,
∞ + ∞ = ∞
∞⋅L = ∞ and
∞/L = ∞ for all positive L
∞⋅L = −∞ and
∞/L = −∞ for all negative L
∞⋅∞ = ∞
1/0+ = ∞ and
1/0- = −∞,
L/∞ = 0 for all real
L
∞L = ∞
for all positive L,
∞L = 0
for all negative L
L∞ = ∞ if
L > 1,
L∞ = 0 if
|L| < 1, and
L∞ DNE if L < −1
L−∞ = 0
if |L| > 1,
L−∞ = ∞ if
0 < L < 1, and
L−∞ DNE if
−1 < L < 0
∞∞ = ∞
e∞ = ∞, e−∞ = 0,
ln(∞) = ∞,
ln(0+) = −∞
For more details on limit algebra, see
here.