# limit rules - rmlowman/math165/lecturenotes/l5-w2l2r · limit rules example lim x!3 x2 9 x 3 =?...

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Limit RulesUseful rules for finding limits:

In the following rules assume k = constant

limxc

k = k

limxc

kf(x) = k limxc

f(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x)

g(x)=

limxc f(x)

limxc g(x)( 6=0)

limxc

[f(x)n] =[limxc

f(x)]n

limxc

P(x) = P(c) , P(x) is continuous around c, just plug-in

Limit RulesUseful rules for finding limits:In the following rules assume k = constant

limxc

k = k

limxc

kf(x) = k limxc

f(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x)

g(x)=

limxc f(x)

limxc g(x)( 6=0)

limxc

[f(x)n] =[limxc

f(x)]n

limxc

P(x) = P(c) , P(x) is continuous around c, just plug-in

Limit RulesUseful rules for finding limits:In the following rules assume k = constant

limxc

k = k

limxc

kf(x) = k limxc

f(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x)

g(x)=

limxc f(x)

limxc g(x)( 6=0)

limxc

[f(x)n] =[limxc

f(x)]n

limxc

P(x) = P(c) , P(x) is continuous around c, just plug-in

Limit RulesUseful rules for finding limits:In the following rules assume k = constant

limxc

k = k

limxc

kf(x) = k limxc

f(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x)

g(x)=

limxc f(x)

limxc g(x)( 6=0)

limxc

[f(x)n] =[limxc

f(x)]n

limxc

P(x) = P(c) , P(x) is continuous around c, just plug-in

Limit RulesUseful rules for finding limits:In the following rules assume k = constant

limxc

k = k

limxc

kf(x) = k limxc

f(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x)

g(x)=

limxc f(x)

limxc g(x)( 6=0)

limxc

[f(x)n] =[limxc

f(x)]n

limxc

P(x) = P(c) , P(x) is continuous around c, just plug-in

Limit RulesUseful rules for finding limits:In the following rules assume k = constant

limxc

k = k

limxc

kf(x) = k limxc

f(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x)

g(x)=

limxc f(x)

limxc g(x)( 6=0)

limxc

[f(x)n] =[limxc

f(x)]n

limxc

P(x) = P(c) , P(x) is continuous around c, just plug-in

Limit RulesUseful rules for finding limits:In the following rules assume k = constant

limxc

k = k

limxc

kf(x) = k limxc

f(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x)

g(x)=

limxc f(x)

limxc g(x)( 6=0)

limxc

[f(x)n] =[limxc

f(x)]n

limxc

P(x) = P(c) , P(x) is continuous around c, just plug-in

Limit RulesUseful rules for finding limits:In the following rules assume k = constant

limxc

k = k

limxc

kf(x) = k limxc

f(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x)

g(x)=

limxc f(x)

limxc g(x)( 6=0)

limxc

[f(x)n] =[limxc

f(x)]n

limxc

P(x) = P(c) , P(x) is continuous around c, just plug-in

Limit RulesUseful rules for finding limits:In the following rules assume k = constant

limxc

k = k

limxc

kf(x) = k limxc

f(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x) g(x) = limxc

f(x) limxc

g(x)

limxc

f(x)

g(x)=

limxc f(x)

limxc g(x)( 6=0)

limxc

[f(x)n] =[limxc

f(x)]n

limxc

P(x) = P(c) , P(x) is continuous around c, just plug-in

Limit Rulesexample

limx3

x2 9x 3

=?

first try limit of ratio = ratio of limits rule,

limx3

x2 9x 3

=limx3 x2 9limx3 x 3

=0

0

00 is called an indeterminant form. When you reach an indeterminant formyou need to try someting else.

limx3

x2 9x 3

= limx3

(x 3)(x + 3)(x 3)

= limx3

(x + 3) = 3 + 3 = 6

Indeterminant does not mean the limit does not exist.It just means that the method you tried did not tell you anythingand you need to try another method.

Limit Rulesexample

limx3

x2 9x 3

=?

first try limit of ratio = ratio of limits rule,

limx3

x2 9x 3

=limx3 x2 9limx3 x 3

=0

0

00 is called an indeterminant form. When you reach an indeterminant formyou need to try someting else.

limx3

x2 9x 3

= limx3

(x 3)(x + 3)(x 3)

= limx3

(x + 3) = 3 + 3 = 6

Indeterminant does not mean the limit does not exist.It just means that the method you tried did not tell you anythingand you need to try another method.

Limit Rulesexample

limx3

x2 9x 3

=?

first try limit of ratio = ratio of limits rule,

limx3

x2 9x 3

=

limx3 x2 9limx3 x 3

=0

0

00 is called an indeterminant form. When you reach an indeterminant formyou need to try someting else.

limx3

x2 9x 3

= limx3

(x 3)(x + 3)(x 3)

= limx3

(x + 3) = 3 + 3 = 6

Indeterminant does not mean the limit does not exist.It just means that the method you tried did not tell you anythingand you need to try another method.

Limit Rulesexample

limx3

x2 9x 3

=?

first try limit of ratio = ratio of limits rule,

limx3

x2 9x 3

=limx3 x2 9limx3 x 3

=

0

0

limx3

x2 9x 3

= limx3

(x 3)(x + 3)(x 3)

= limx3

(x + 3) = 3 + 3 = 6

Limit Rulesexample

limx3

x2 9x 3

=?

first try limit of ratio = ratio of limits rule,

limx3

x2 9x 3

=limx3 x2 9limx3 x 3

=0

0

limx3

x2 9x 3

= limx3

(x 3)(x + 3)(x 3)

= limx3

(x + 3) = 3 + 3 = 6

Limit Rulesexample

limx3

x2 9x 3

=?

first try limit of ratio = ratio of limits rule,

limx3

x2 9x 3

=limx3 x2 9limx3 x 3

=0

0

00 is called an indeterminant form.

When you reach an indeterminant formyou need to try someting else.

limx3

x2 9x 3

= limx3

(x 3)(x + 3)(x 3)

= limx3

(x + 3) = 3 + 3 = 6

Limit Rulesexample

limx3

x2 9x 3

=?

first try limit of ratio = ratio of limits rule,

limx3

x2 9x 3

=limx3 x2 9limx3 x 3

=0

0

limx3

x2 9x 3

= limx3

(x 3)(x + 3)(x 3)

= limx3

(x + 3) = 3 + 3 = 6

Limit Rulesexample

limx3

x2 9x 3

=?

first try limit of ratio = ratio of limits rule,

limx3

x2 9x 3

=limx3 x2 9limx3 x 3

=0

0

limx3

x2 9x 3

=

limx3

(x 3)(x + 3)(x 3)

= limx3

(x + 3) = 3 + 3 = 6

Limit Rulesexample

limx3

x2 9x 3

=?

first try limit of ratio = ratio of limits rule,

limx3

x2 9x 3

=limx3 x2 9limx3 x 3

=0

0

limx3

x2 9x 3

= limx3

(x 3)(x + 3)(x 3)

=

limx3

(x + 3) = 3 + 3 = 6

Limit Rulesexample

limx3

x2 9x 3

=?

first try limit of ratio = ratio of limits rule,

limx3

x2 9x 3

=limx3 x2 9limx3 x 3

=0

0

limx3

x2 9x 3

= limx3

(x 3)(x +

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