Middleton High School PreCalculus Questions Several different questions all about precalculus. Need work to be shown for all questions. take for the popula

Middleton High School PreCalculus Questions Several different questions all about precalculus. Need work to be shown for all questions. take for the population of the bacteria to reach
520?
1. To find the distance AB across a river, a distance AC
of 783 meters is laid off on one side of the river. It is
found that = 108° and = 17°. Find the
distance across the river from A to B.
6. Solve the equation 28 = 2 0.42 − 7
7. Convert the rectangular coordinate (−2, 2√3) using
three different polar representations of the point.
2. Sasha is outside of a building. She sees Thomas on
the 4th floor at an angle of elevation (from ground
level) of 48°. She then sees Sebastian on the 9th
floor at an angle of elevation of 67°. If Thomas is 52
feet from ground level, what is the distance from
Thomas to Sebastian?
8. Convert the polar coordinates into rectangular
coordinates.
2
(a) (−8, 5 )
(b) (7, −73°)
Given
⃗ = 〈2, −4〉 and = 〈3, 1〉, find:
9. ||
⃗ ||
3. A baseball player in center field is approximately
330 feet from a television camera that is behind
home plate. A batter hits a fly ball that goes to the
wall 420 feet from the camera. The camera turns 8°
to follow the play. Approximately how far goes the
center fielder have to run to make the catch?
10. The direction angle of
⃗
11. The direction angle of
Write the following complex numbers in trig form:
12. −5 + 2
13. 3 − √3
4. Tampa is 86 miles from Orlando. Orlando is 244
miles from Miami and Miami is 295 miles from
Tampa. At Orlando, what is the angle from Tampa
to Miami?
14. −1 −
Given = 〈−3, 3〉 and = 〈4, 5〉, find:
15. ⃗⃗⃗⃗
2 − 3
16. 3|| ||
17. ||4 ||
5. The population of a certain bacteria growth over
time in minutes can be given by the equation,
= 32 ln − 5, where > 0. How long would it
Evaluate the following limits:

→0
18. lim
1
( +1)

→∞
19. lim
−2 2 +3 −4
3 −5
→∞
21. lim+
20. lim
→0
| +2|

37. 3 = 1
Evaluate each of the following:
1
23. −1 (−1)
22. −1 (− )
38. 2 = −
2
24. −1 (2)
25. −1 (−√3)
26. −1 (1)
28.
27. −1 (−
√2
[ −1 ( )]
2
30. Simplify cos ( −
29.
−1
39. 2 − √3 = 0
√2
)
2
40. Find the general solution of 2 2 = 2 .
5
( )
4
3
)
2
Given =
41. (2 )
11
12
32.
7
12

and 0

-0.1
( ) 2.218
–0.01
2.220
–0.001
2.222
0
error
0.001
2.226
0.01
2.228
0.1
2.230
For what values of is not continuous?
73. Given the following table
3
what is the value of lim ( ) ?
→0
2 −36
→6 −6
77. Find lim
76. Find lim
→
74. Given the graph of ( )
2 3 +3 −18
→∞ 8 −4 4 + 2
3 +7 2 +10
→0 3 − 2 −6
78. Find lim
79. Find lim
80. Which function is NOT continuous at = 2?
A) ( ) = 2 − 4 + 4
a. For
what
value(s) of
is ( )
B) ( ) =
2 −4 +4
+2
C) ( ) =
2 −4
+2
D) ( ) =
2 −4
−2
81. Given that is a continuous function on the interval
[1,5] and (1) = −1 and (5) = 7, what does the
IVT (Intermediate Value Theorem) guarantee for the
function ?
discontinuous?
b. What is lim ( ) ?
→3
82. Using the IVT (Intermediate Value Theorem) given
( ) = 2 2 − − 5 is a continuous function, does
( ) have a zero over the interval [−3, 1]? Why or
why not?
c. What is lim ( ) ?
→0
75. Given the graph of ( )
83. Use the DEFINITION of continuity to determine if
( ) is continuous at = 2. Explain.
For what value(s) of is ( ) discontinuous?
A) −2
B) 3
C) −2, 3
D) no points of discontinuity
84. If lim ( ) = 4 and lim ( ) = 7,
→
→
Find:
( )
a. lim ( )
→
4
b. lim ( ) ∙ ( )
→
c. lim 5 ( )
→
85. What domain restrictions must be placed on all
six trigonometric functions so that their
inverses can be defined.
86. Write the equation of the following polar
graphs:
a.
b.
5

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