[limits at infinity][section 2]

(1.) lim (1/x⁴) here is the problem
x->0

= ∞

(2.) lim (1/x⁵) here is the problem
x->0

= DNE (does not exist)

[because, the limit is different coming in from the left of

0, as it is coming in from the right of 0]

(3.) lim [1/(x - 5)³] here is the problem
x->5

= DNE (does not exist)

(4.) lim (x + x²)/(x² + x³) here is the problem
x->0

= lim (1 + x)/(x + x²) divide thru by x, cancel

= lim (1/x)(1 + x)/(1 + x) factor

= lim (1/x) cancel
x->0

= DNE

(5.) lim (x - 4)/(x + 3)²
x->-3

= ∞

(6.) lim x/(1 + x)
x->∞

= 1


_
(7.) lim [1/(1 - √x)]
x->∞

= 0

(8.) lim (2x + 3)/(3x + 2)
x->∞

= 2/3

(9.) lim (5x - x²)/(3x + x²)
x->∞

= -1

(10.) lim [2x² + 3x + 5]
x->∞ ______________
[3x² - x + 2]

= 2/3