Name _____KEY__________

PreCalculus – Chapter 11 Test Review – Limits and Calculus All questions worth 1 point unless otherwise stated. Total 34 points.

Find the following limits using the figure to the right. ( ) 1. 1 2.

( )

3.

( ) ( )

4. 5.

( )

No Limit 1

6.

( )

1

( )

7.

1

8.

( )

9.

( )

1 No Limit

( )

10.

Find the following limits. ( ) 11.

49

12. 13. Decompose the following fractions. 14. 15. ( 16.

)(

)

( 2 points)

Review. Perform the following computations. 17. [

]

18. [

[

[

]

][

[

]

]

]

[

]

19. If AB = BA what do you know about matrices A and B? They are inverses of each other. 20. What are two reasons why some matrices don’t have inverses? The determinant could be zero, or they might not be square. Find the determinants and inverses of the following matrix. 21. [

(2 points)

] [

156+192+192 208+192+144 544-540 Solve the following system.

[

]

]

Many elementary row operations that will require extra paper [

[

22.

[

]

]

[

]

]

[

[

]

]

(

)

[

][

]

1 ***3 possible extra credit points : do #21, 22 by hand. You can use a calculator to check.***

Switch between polar form (trigonometric form) and rectangular form (a+bi form). ( ) √( ) 23. √ (

)

24.

)

√(

25. (

)

( )



)

27. ( (

)) ( √ (

28. ( (

))

29. √ (



(2 points)

Find the angle between the vectors. 〉 〉〈

















) or √

(

) 〉〈

√ (

))

)

√ (

31. 〈

(

)

26. ( Simplify.

30. 〈



) √



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