Let P ( x 0 , f ( x 0 ) ) be a fixed point on the graph of the differential function f with a domain that is the set of real numbers. Determine the real number z 0 such that point Q ( x 0 + 1 , z 0 ) is situated on the line tangent to the graph of f at point P . Determine the unit vector u with initial point P and terminal point Q .
Let P ( x 0 , f ( x 0 ) ) be a fixed point on the graph of the differential function f with a domain that is the set of real numbers. Determine the real number z 0 such that point Q ( x 0 + 1 , z 0 ) is situated on the line tangent to the graph of f at point P . Determine the unit vector u with initial point P and terminal point Q .
Let
P
(
x
0
,
f
(
x
0
)
)
be a fixed point on the graph of the differential function
f
with a domain that is the set of real numbers.
Determine the real number
z
0
such that point
Q
(
x
0
+
1
,
z
0
)
is situated on the line tangent to the graph of
f
at point
P
.
Determine the unit vector
u
with initial point
P
and terminal point
Q
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Example 4 (Part 2) We can use Statkey to take 50 different random samples of size 20 each, find the mean of
each sample, and compute a confidence interval for each one. The graph of the sampling distribution of the means
is on the left below, and that of the 50 confidence intervals is on the right.
1. What does each dot on the left hand dotplot represent?
StatKey Sampling Distribution for a Mean
Percent with Internet Access (Countries) ▾
Show Data Table Edit Data
Choose samples of size n =
20
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Change Column(s)
Generate 1 Sample
Generate 10 Samples
Generate 100 Samples
Generate 1000 Samples
Reset Plot
Sampling Dotplot of Mean
Left Tail Two-Tail Right Tail
60
50
40
40
30
20
20
10
samples = 50
mean = 41.626
std. error = 5.089
:
.:
:
::
0
25
30
35
40
45
50
55
60
41.626
Data Plots
Confidence Intervals
95%->
Confidence Intervals
Coverage
48/50 = 96%
20
40
60
80
2. Circle the confidence intervals that failed to capture the true mean.
3. Circle the sample means that produced those…
College Algebra with Modeling & Visualization (5th Edition)
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