AB Calculus AB Unit 1 Packet Name:___________________

PUSHED BEYOND THE LIMIT?

First, find the limits of each problem. Put the answers in order from least to greatest, using the letter corresponding with the problem. If a limit does not exist, it will go at the END. There are four that DNE…you must put them in order to spell the last word.

Using the graph above, Using the graph above,

E) E) O) R)

R)L) I) T)

N)E) M) H)

A)I) I) E)

1

Using the graph to the left, find the limit of:

T)

L)

F)

I)

S)

N)

____ ____ ____ ____ ____ ____ ____ ____ ____ ____

____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____!

AB CalculusSolving Limits Algebraically

Find the following limits:

2

1. 2.3.

4. 5. 6.

7. 8. 9.

10. 11.12.

13.14. 15.

16.

17. 18.

19.20.

21.

22. 23. 24.

25. 26.

27. Find where

28. Find the right hand limit at x = 1 for

29. Find the left hand limit at x = 0 for AB CALCULUSVersatiles Activity: LIMITS

Find each Limit3

1. limx→−1

x+ x2

x2−1 = 7. limn→∞

3n3−5nn3−2n2+1 =

2. If limn→∞

6n2

200−4 n+kn2=1

2 , then k = 8. limx→∞

(1−2x2 )3

(x2+1)3 =

3. limx→0xcsc x

=

9. limx→1

1x+1

−12

x−1 =

4. limx→9

x−93−√ x = 10.

limx→0

1−cos x2 sin2 x =

5. limx→∞

( 1x− xx−1

)= 11.

limx→0

cos2( x )−12 x sin x =

6. limx→1

xln x = 12.

limx→−2

x2−4x+2 =

ANSWERS

A B C D E FG H I J K L

Calculus ABContinuity Practice

123 -6 -4 −14

1 -1 nonexistent-8

12

14

−12

4

Find all the graphs with jump discontinuity. _________________________________

Find all the graphs with removable discontinuity. ____________________________

Find all graphs with infinite discontinuity. _________________________________

Find all graphs that are continuous on the entire domain. _____________________

AB CalculusLimits Involving Infinity

Complete the limits and find ALL horizontal and vertical asymptotes for the following functions. DO THIS WITHOUT A CALCULATOR.

5

1.

2.

3.

4.

5.

6.

7.

Continuity and Limits Match-UpSolve the following problems, find the answers from the right and put the letter in the blank. Use these letters to fill in the puzzle at the end!

_________ 1. Test for continuity at x = - 2: A. 2

6

Find the horizontal asymptote: Write the horizontal asymptote as a limit:

Find the vertical asymptote(s): Write the vertical asymptote(s) as limits:

Find the horizontal asymptote: Write the horizontal asymptote as a limit:

Find the vertical asymptote(s): Write the vertical asymptote(s) as limits:

Find the horizontal asymptote: Write the horizontal asymptote as a limit:

Find the vertical asymptote(s): Write the vertical asymptote(s) as limits:

Find all horizontal and vertical asymptotes. JUSTIFY your answer using a limit definition.

_________ 2. Test for Continuity at x = 1: C. -2.5

_________ 3. D. 0

_________ 4. E. 4

_________ 5. F.

_________ 6. H. 36

_________ 7. Test for continuity at x = 2: I.

_________ 8. J. Continuous at x = 1

_________ 9. K. Not Continuous at x = 1

_________ 10. L. Does Not Exist

_________ 11. M. -8

_________ 12. N. Continuous atx = 5

_________ 13. Test for continuity at x = -2: O. Continuous atx = 2

_________ 14. P. Not Continuous at x = 5

_________ 15. Test for continuity at x = 2: R. Not Continuous at x = 2

7

_________ 16. Test for continuity at x = 5: S. 14

_________ 17. T.

_________ 18. U. 11

V. Not Continuous At x = -2

Y. Continuous at x = -2

Write the corresponding letter to each problem in the spaces below.

_____ _____ _____ _____ _____ _____ _____ 7 5 3 10 9 18 17

_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ 18 14 9 8 17 14 15 6 16 14 13 14 15

_____ _____ _____; _____ _____ _____ _____ _____ _____ _____ _____ 3 12 14 18 17 14 1 2 4 6 18

_____ _____ _____ _____ _____ _____18 14 16 3 18 7

_____ _____ _____ _____ _____ _____ _____ _____!! 12 16 11 12 16 12 18 1

8

Practice with Limits and Continuity

1. Is continuous at ? Justify your answer.

2. Find the value of so is continuous.

3. Find given and .

4. Is continuous at ? Is continuous at ?

5. Given is continuous on , what is the minimum number of times ?

0 2 3 4 5

-2 0 3 -4 2

6. Given: a. Find the domain.b. Write an equation for the vertical and horizontal asymptote(s).c. Is there a removable point of discontinuity? If so, identify the location.

d. Evaluate:

e. Evaluate:

f. Evaluate:

9

g. Evaluate: h. Is the function even, odd, or neither?

7. Evaluate:

8. Evaluate:

9. Evaluate:

10. Evaluate:

11. Evaluate:

12.

Evaluate:

10