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

Post on 05-Feb-2018

215 views

Category:

## Documents

Embed Size (px)

TRANSCRIPT

• 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

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

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

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 +