01 - Limits At Removable Discontinuities.pdf 25413h

Kuta Software - Infinite Calculus

Name___________________________________

Evaluating Limits

Date________________ Period____

Evaluate each limit. 1) lim f ( x) , f ( x) = x→2

− x 2 + 2, x ≠ 2

{

−5,

x=2

2) lim − x → −2

x2 − 4 x+2 f(x)

f(x)

12

4 10 2 8 −6

−4

−2

2

4

6

8

10 x

6

−2 4 −4 2 −6 −10

−8

−6

−4

−2

2

4

6 x

−8 −2 −10 −4

Evaluate each limit. You may use the provided graph to sketch the function. x 2 − 7 x + 12 3) lim x→3 x−3

4) lim

x → −3

x+3 x + 2x − 3 2

f(x)

f(x) 8

6 6 4 4 2 2 −4

−2

2

4

6

8

10

x −10

−2

−8

−6

−4

−2

2

4

x

−2 −4 −4 −6 −6 −8 −8

Evaluate each limit. 5) lim f ( x) , f ( x) = x→0

{

x + 1, x ≠ 0

2,

x=0

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6) lim f ( x) , f ( x) = x→3

-1-

{

2+ 2,

x , x≠3 2 x=3

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x2 − 1 7) lim − x→1 x−1

x2 − 5x 8) lim − x→5 x−5

x2 − x − 2 9) lim − x→2 x−2

x 2 + 3 x − 10 10) lim x → −5 x+5

1 1 + −4 + x 4 11) lim x→0 x

13) lim x→5

x−5 x+4 −3

12) lim

x → −3

14) lim x→3

x 1 1 − 3+x 3

x+6 −3 x−3

Critical thinking questions: 15) Give an example of a limit of a rational function where the limit at -1 exists, but the rational function is undefined at -1.

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16) Give two values of a where the limit cannot be solved using direct evaluation. Give one value of a where the limit can be solved using direct evaluation. x lim → x a 1 1 + −2 + x 2

-2-

Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Name___________________________________

Evaluating Limits

Date________________ Period____

Evaluate each limit. 1) lim f ( x) , f ( x) = x→2

− x 2 + 2, x ≠ 2

{

−5,

x=2

2) lim − x → −2

x2 − 4 x+2 f(x)

f(x)

12

4 10 2 8 −6

−4

−2

2

4

6

8

10 x

6

−2 4 −4 2 −6 −10

−8

−6

−4

−2

2

4

6 x

−8 −2 −10 −4

4

−2

Evaluate each limit. You may use the provided graph to sketch the function. x 2 − 7 x + 12 3) lim x→3 x−3

4) lim

x → −3

x+3 x + 2x − 3 2

f(x)

f(x) 8

6 6 4 4 2 2 −4

−2

2

4

6

8

10

x −10

−2

−8

−6

−4

−2

2

4

x

−2 −4 −4 −6 −6 −8 −8

−1

−

1 4

Evaluate each limit. 5) lim f ( x) , f ( x) = x→0

{

x + 1, x ≠ 0

2,

x=0

6) lim f ( x) , f ( x) = x→3

1

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{

2+ 2,

x , x≠3 2 x=3

7 2

-1-

Worksheet by Kuta Software LLC

x2 − 1 7) lim − x→1 x−1

x2 − 5x 8) lim − x→5 x−5

−2

−5

x2 − x − 2 9) lim − x→2 x−2

x 2 + 3 x − 10 10) lim x → −5 x+5

−3

−7

1 1 + −4 + x 4 11) lim x→0 x −

12) lim

x → −3

x→5

1 1 − 3+x 3

0

1 16

13) lim

x

x−5 x+4 −3

14) lim x→3

6

x+6 −3 x−3

1 6

Critical thinking questions: 15) Give an example of a limit of a rational function where the limit at -1 exists, but the rational function is undefined at -1. x2 − 1 Many answers. Ex: lim x → −1 x + 1

16) Give two values of a where the limit cannot be solved using direct evaluation. Give one value of a where the limit can be solved using direct evaluation. x lim → x a 1 1 + −2 + x 2 No direct eval: a=0,2 Direct eval: a=any other number

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-2-

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