Limits and Continuity

0

3 3limx

x

x

3

6

0

lim csc6 tan5x

x x

5

6

1

2

24

2 7 4lim

20x

x x

x x

0

lim8 cot 3x

x x

8

3

1 15 5

0lim x

x x

1

25

A. f(x) =-5B. f(x) = 4C. f(x) = -1D. f(x) = 0E. no horizontal asymptotes

D

2

3

5 4

1

x xf x

x

25

2lim

3 10x

x

x x

Does Not Exist

2

lim 1x

x

1

limx

f x

1

x

y

13

2

4, 3

2 , 3

4 , 3

x x

f x x x

x x

3

limx

f x

5

24lim

2 5x

x

x

1

lim 2 4x

x

8

A. f(x) = -2B. f(x) = -1C. f(x) = 1/8D. f(x) = 3E. No horizontal asymptotes

A

2

2

2 3 1( )

16

x xf x

x

2 , 2

1, 2

ax xf x

ax x

1/6

A. ContinuousB. Discontinuous non-removable at x = -6C. Discontinuous removable at x = -6D. Discontinuous non-removable at x = 0

C

23 18

6

x x

x

A. ContinuousB. Discontinuous removable at x = -4C. Discontinuous removable at x = 4D. Discontinuous non-removable at x = 4E. Both B and CF. Both B and D

B

2 16( )

9 36

xf x

x