[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
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(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
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(9.) lim (√x + 4) here is the problem
x->-4
_______
= √-4 + 4 replace x with -4
_
= √0 add

= 0 take square root

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(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