[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
= 2 add
(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 add
= 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