Evaluating Limits Date Period - Kuta Software

Kuta Software - Infinite Calculus

Name___________________________________

Evaluating Limits

Date________________ Period____

Evaluate each limit.

1) lim+

x ¡ú ?1

4x + 4

2) lim? f ( x) , f ( x) =

x+1

x ¡ú ?1

8

4

6

2

4

?8

?6

?4

?4

2

2

4

6

6

x

?4

x

?2

?6

?4

?8

?6

?10

?8

?12

x ¡ú ?3

4

?2

?2

3) lim f ( x) , f ( x) =

? x 2 ? 4 x ? 4, x > ?1

?2

2

?6

x ¡Ü ?1

f(x)

f(x)

?8

{

? x ? 8,

? x 2 ? 10 x ? 24, x ¡Ü ?3

{

2 x + 3,

x > ?3

4) lim f ( x) , f ( x) =

x ¡ú ?1

f(x)

{

x < ?1

x,

2

? x + 2 x, x ¡Ý ?1

f(x)

6

4

4

2

2

?10

?8

?6

?4

?2

2

4

x

?8

?2

?6

?4

?2

2

4

6

x

?2

?4

?4

?6

?6

?8

?8

?10

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?10

-1-

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Evaluate each limit. You may use the provided graph to sketch the function.

5) lim? f ( x) , f ( x) =

x ¡ú ?1

{

? x ? 3, x ¡Ü ?1

x + 1, x > ?1

6) lim f ( x) , f ( x) =

x ¡ú ?2

? x 2 ? 4 x ? 5, x ¡Ü ?2

{

f(x)

?8

?6

?4

f(x)

6

6

4

4

2

2

?2

x > ?2

?1,

2

4

6

?10

x

?8

?6

?4

?2

2

?2

?2

?4

?4

?6

?6

?8

?8

4

6 x

Evaluate each limit.

7) lim+ f ( x) , f ( x) =

x¡ú0

{

1,

x¡Ü0

2

? x + 4 x ? 3, x > 0

9) lim+ ?2 x + 1

x¡ú0

8) lim?

x¡ú0

x ¡ú ?1

x

10) lim f ( x) , f ( x) =

x¡ú1

11) lim

x

{

3 x+1

x+1

12) lim f ( x) , f ( x) =

x ¡ú ?2

x 9

+ ,

2 2

x ?2

2

Critical thinking questions:

13) Give an example of a two-sided limit of a

piecewise function where the limit does not

exist.

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14) Given an example of a two-sided limit of a

function with an absolute value where the limit

does not exist.

-2-

Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Name___________________________________

Evaluating Limits

Date________________ Period____

Evaluate each limit.

1) lim+

x ¡ú ?1

4x + 4

2) lim? f ( x) , f ( x) =

x+1

x ¡ú ?1

8

4

6

2

4

?8

?6

?4

?4

? x 2 ? 4 x ? 4, x > ?1

?2

2

4

6

x

?2

2

?6

x ¡Ü ?1

f(x)

f(x)

?8

{

? x ? 8,

?2

2

4

6

?4

x

?2

?6

?4

?8

?6

?10

?8

?12

?7

4

3) lim f ( x) , f ( x) =

x ¡ú ?3

? x 2 ? 10 x ? 24, x ¡Ü ?3

{

2 x + 3,

x > ?3

4) lim f ( x) , f ( x) =

x ¡ú ?1

f(x)

{

x < ?1

x,

2

? x + 2 x, x ¡Ý ?1

f(x)

6

4

4

2

2

?10

?8

?6

?4

?2

2

4

x

?8

?2

?6

?4

?2

2

4

6

x

?2

?4

?4

?6

?6

?8

?8

?10

?10

Does not exist.

?3

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-1-

Worksheet by Kuta Software LLC

Evaluate each limit. You may use the provided graph to sketch the function.

5) lim? f ( x) , f ( x) =

x ¡ú ?1

{

? x ? 3, x ¡Ü ?1

6) lim f ( x) , f ( x) =

x + 1, x > ?1

x ¡ú ?2

? x 2 ? 4 x ? 5, x ¡Ü ?2

{

f(x)

?8

?6

?4

f(x)

6

6

4

4

2

2

?2

x > ?2

?1,

2

4

6

?10

x

?8

?6

?4

?2

2

?2

?2

?4

?4

?6

?6

?8

?8

?2

4

6 x

?1

Evaluate each limit.

7) lim+ f ( x) , f ( x) =

x¡ú0

{

1,

x¡Ü0

8) lim?

2

? x + 4 x ? 3, x > 0

x¡ú0

?3

x

x

?1

9) lim+ ?2 x + 1

x¡ú0

10) lim f ( x) , f ( x) =

x¡ú1

0

{

x 9

+ ,

2 2

x ?2

2

4

Critical thinking questions:

13) Give an example of a two-sided limit of a

piecewise function where the limit does not

exist.

Many answers. Ex: lim f ( x) , f ( x) =

x¡ú1

{

14) Given an example of a two-sided limit of a

function with an absolute value where the limit

does not exist.

0, x < 1

Many answers. Ex: lim

x¡ú0

x, x ¡Ý 1

x

x

Create your own worksheets like this one with Infinite Calculus. Free trial available at

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Worksheet by Kuta Software LLC

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