IXL - Find limits using limit laws (Precalculus practice)

lim

→8

(

)

lim

→8

(

)

–

and

lim

→8

(

)

what is

lim

→8

[

(

)

–

(

)

(

)

]

Simplify your answer.

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Learn with an example

question

lim

→0

(

)

lim

→0

(

)

–

and

lim

→0

(

)

what is

lim

→0

[

(

)

–

(

)

(

)

]

Simplify your answer.

key idea

lim

→

(

)

and

lim

→

(

)

where

and

are real numbers, then the following statements are true:

lim
x
→
a
[
u
(
x
)
±
v
(
x
)
]
=
lim
x
→
a
u
(
x
)
±
lim
x
→
a
v
(
x
)
=
L
±
M
lim
x
→
a
[
u
(
x
)
v
(
x
)
]
=
lim
x
→
a
u
(
x
)
lim
x
→
a
v
(
x
)
=
L
M
lim
x
→
a
u
(
x
)
v
(
x
)
=
lim
x
→
a
u
(
x
)
lim
x
→
a
v
(
x
)
=
L
M
(whenever
M
≠
0
)

solution

You know that

lim

→0

(

)

lim

→0

(

)

–

and

lim

→0

(

)

Since each limit exists and is finite, the appropriate limit laws can be combined to evaluate the limit.

lim

→0

[

(

)

–

(

)

(

)

]

Limit law for subtraction

lim

→0

(

)

–

lim

→0

[

(

)

(

)

]

Limit law for subtraction

Limit law for multiplication

lim

→0

(

)

–

lim

→0

(

)

lim

→0

(

)

Limit law for multiplication

–

(

–

)

The limit is 38.

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Not feeling ready yet? These can help:

HH.8Find limits using power and root laws

HH.7Find limits using the division law

HH.6Find limits using addition, subtraction, and multiplication laws

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