Math 153 Final Exam Extra Review Problems Worksheet Page 8
ADVERTISEMENT
1
2
3
4
5
6
7
860. The height of a wave (in inches, after t seconds) is given by ( ) = 5
( 4 ) What’s the height
initially? What happens to the height as t increases? Explain your reasoning.
61. Sketch the curve represented by the parametric equations x = t − 5, y = √ t − 2. Find a rectangular
coordinate equation for the curve by eliminating the parameter.
62. Sketch the curve represented by the parametric equations x = 6 sin , y = 6 cos . Find a
rectangular coordinate equation for the curve by eliminating the parameter.
63. Sketch the curve represented by the parametric equations x = cos , y = 1 + cos
. Find a
rectangular coordinate equation for the curve by eliminating the parameter.
64. Find parametric equations for a line passing through (-2,-8) and (-5,1). Find a rectangular coordinate
equation for the curve by eliminating the parameter.
+
= 4.
65. Find parametric equations for the circle
66. Convert each point in rectangular coordinates to polar coordinates with
>
and
≤
<
.
(x, y) = (-3, 3),
(x, y) = (4 √ 3, -4),
(x, y) = (0, -10)
67. Convert the polar coordinates to rectangular coordinates (x, y)
( , ) = ( 5,0 ) ,
( , ) = −2,
,
( , ) = −1,
68. Convert each equation to rectangular form, simplify, and graph:
= − ,
= 7,
cos = −1
69. Evaluate/Simplify. Write your answer in the form a + bi: ( − )
+ (3 − ),
,
70. For each complex number, graph, find the modulus and the conjugate: z = −8 + 6i, = −3
71. Write each in polar form with 0 ≤
< 2 , > 0:
= 6 − 6 √ 3 ,
= 9,
= −5 + 5
72. For z
= 1 − √ 3, z
= −1 − , find
,
, , ,
. Write all answers with >
and
≤
<
.
1
2
+ ,
−
+ .
73. For each vector, find the magnitude and direction. Graph. Then, find and graph
Practice writing these answers both in component form and in terms of the unit vectors , .
= −4 + 2 ,
= −3 − 3 ,
= −2
74. Express each vector v both in component form and in terms of i and j:
v has length 5 and direction , v has length 1 and direction 330°
75. Find each limit, if it exists
lim
lim
lim
lim
→
→
→
→
lim
lim
− 7
lim
+
lim
→
→
→
→
√ 1 + 5ℎ + 1
ℎ
→
76. For each, find and simplify the difference quotient. Then, find the derivative, ′( ) using the limit
definition.
( ) = −2
( ) =
( ) = √ + 1,
( ) =
+ 3 − 5,
,
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education