IXL - Determine end behavior of polynomial and rational functions (Calculus practice)

Evaluate the limit.

lim

→∞

Simplify any fractions in your answer.

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Learn with an example

question

Evaluate the limit.

lim

→∞

Simplify any fractions in your answer.

key idea

The limit

lim

→∞

(

)

describes the end behavior of

(

)

for positive

-values.

(

)

is the sum, difference, product, or quotient of two functions

(

)

and

(

)

and

lim

→∞

(

)

and

lim

→∞

(

)

are both finite, you can apply valid limit laws to find

lim

→∞

(

)

When

(

)

(

)

(

)

lim

→∞

(

)

is ∞ or

–

∞

and

lim

→∞

(

)

is finite but not zero, you can find

lim

→∞

(

)

using the following rules:

If
lim
x
→∞
g
(
x
)
and
lim
x
→∞
h
(
x
)
have the same sign,
lim
x
→∞
f
(
x
)
is ∞.
If
lim
x
→∞
g
(
x
)
and
lim
x
→∞
h
(
x
)
have opposite signs,
lim
x
→∞
f
(
x
)
is
–
∞
.

is a positive integer, then

lim

→∞

∞

and

lim

→∞

solution

To evaluate

lim

→∞

first evaluate the limits of 6 and

individually.

lim

→∞

lim

→∞

∞

Since 6 is finite but not 0, and has the same sign as ∞,

lim

→∞

∞

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Work it out

Not feeling ready yet? These can help:

B.5Find limits of polynomials and rational functions

D.1Determine end behavior using graphs

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