7/31/2019 Unit 2 - Retakes - Limits & Cont

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Limits Graphically RETAKE NAME: ________________________________________

1. Draw a function on the graph below that satisfies the following:

2. For the graph shown below, determine the limits.

1

lim 1x

1

lim 2x

(2) 3f 2

lim 0x

( 2) 3f 0

limx

0

limx

1

limx

1

limx

2

limx

2

limx

limx

limx

1limx

2

limx

7/31/2019 Unit 2 - Retakes - Limits & Cont

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3.

2

2

2

lim ( )

lim ( )

lim ( )

(2)

x

x

x

d x

d x

d x

d

4

4

4

lim ( )

lim ( )

lim ( )

(4)

x

x

x

d x

d x

d x

d

7/31/2019 Unit 2 - Retakes - Limits & Cont

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Limits Algebraically RETAKE NAME: ________________________________________

1. 22 1lim4x

x

x

2. 46

3 2lim

5 4 1x

x x

x x

3. 3 22

2 1lim

5 3x

x x

x

4.3

4 | 3 |lim

2 6x

x

x

5.1

, 1

lim ( ) 2, 1

2 1, 1x

x x

f x x

x x

6.20

5tanlim

3x

x

x x

7.2

3

4 2lim

5x

x x

x

8.ln

limxx

x x

e

9. 21

3 2lim

1x

x x

x

10.

2

5

x 25, x 5

lim 5

2, x=5x

x

11.2

22

2lim

4 4x

x x

x x

7/31/2019 Unit 2 - Retakes - Limits & Cont

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Intermediate Value Theorem RETAKE NAME: ___________________________________________

1. On which interval does the function f(x) = x3 + 3x 2 have a solution? Show work that leads to your answer.a. (-2, -1) b. (-1, 0) c. (0, 1) d. (1, 2) e. (2, 3)

2. Use the intermediate value theorem to show there is a solution to x4 = 4. Find a one unit interval.

7/31/2019 Unit 2 - Retakes - Limits & Cont

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Continuity RETAKE NAME: _________________________________________

Find any x values for which f(x) is not continuous. State the type of discontinuity. Show all work.

1. 4 | 3 |2 6

x

x

2.2

2 14

x

x

3.2

1, 2 1

2 2, -1 2( )

5, 2

2 10, 2

7/31/2019 Unit 2 - Retakes - Limits & Cont

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BACK--->

4.2

4 9 3

2 3 2( )

37

2

xif x

xf x

if x

Find the values of a and b such that f(x) is continuous for all values of x.

5.2

1, x 1

, -1< 3( )

3 11, 3

x

ax b xf x

x x