[evaluating limits][section 1]

(1.)   lim  (x2 - 6)                here is the problem
x->5

=     (5)2 - 6                   replace x with 5

=     25 - 6               square the 5

=     19                  subtract

(2.)   lim   1/(x5 + 6x + 2)          here is the problem
x->0

=    1/(05 + 6(0) + 2)        replace x with 0

=    1/2                 multiply and combine like terms

(3.)   lim   (x4 - x)/(x3 - 1)         here is the problem
x->1

=      lim  x(x3 - 1)/(x3 - 1)         factor
x->1

=     lim  x                    cancel
x->1

=     1                            replace x with 1

(4.)   lim   (x2 - 4x + 3)/(x - 3)        here is the problem
x->3

=      lim  (x - 3)(x - 1)/(x - 3)       factor
x->3

=       lim (x - 1)           cancel
x ->3

=       3 - 1             replace x with 3

=      2              subtract

(5.)   lim  (x2 + 6x + 8)/(x + 2)         here is the problem
x-> -2

=     lim (x + 2)(x + 4)/(x + 2)           factor
x->-2

=     lim (x + 4)                    cancel
x->-2

=     -2 + 4                replace x with -2

(6.)   lim  (√x - 1)/(x - 1)        here is the problem
x->1
_        _       _
=    lim  (√x - 1)/(√x - 1)(√x + 1)   factor
x->1
_
=     lim  [1/(√x + 1)]              cancel
x->1
_
=     1/(√1 + 1)            replace x with 1

=    1/2           take square root and add
___
(7.)   lim   (1 - √x/2)/(2 - x)       here is the problem
x->2
___
=      lim   (1/2)(1 - √x/2)/[1 - (x/2)]   factor
x->2
___         ___       ___
=     lim (1/2)(1 - √x/2)/[(1 - √x/2)(1 + √x/2)]  factor
x->2
___
=     lim  (1/2)/[1 + √x/2]    cancel
x->2
___
=    (1/2)/(1 + √2/2)          replace x with 2

=   (1/2)/(2)            divide, take square root, add

=  1/4                     divide

(8.)   lim (x4 - 9)          here is the problem
x->2

=     24 - 9                replace x with 2

=   16 - 9             raise 2 to the 4th power

=    7                 subtract
_____
(9.)   lim (√x + 4)          here is the problem
x->-4
_______
=     √-4 + 4          replace x with -4
_

=   0                 take square root

______
(10.)  lim  \3/x3 - 8          here is the problem
x->2
______
=    \3/23 - 8            replace x with 2
_____
=     \3/8 - 8             cube 2
_
=   \3/0               subtract

=   0                  take cube root