Turunan pertama dari y=3x+5x+2 adalah
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Category: Mathematics
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Inductive and Deductive Reasoning, Stereotyping, Prejudging
Instructions: Type your answers to the questions below. Save your file as Word or PDF file titled MAT107project. Uploading for assessment purposes is discussed in class (Wait for the instructor to explain the process to you). MAT107 Inquiry and Problem Solving Project / Writing Ability Inductive and Deductive Reasoning: Generalizations, Assumptions, … Stereotyping refers to classifying people, places, or things according to common traits. Prejudices and stereotypes can function as assumptions in our thinking, appearing in inductive and deductive reasoning. For example, it is not difficult to find inductive reasoning that results in generalizations such as these, as well as deductive reasoning in which these stereotypes serve as assumptions: School has nothing to do with life. Intellectuals are nerds. People on welfare are lazy. 1) Using information from the internet and other reliable sources, define the terms stereotyping and prejudging. Please cite your sources. 2) Using what you learned in this class, define the terms inductive and deductive reasoning. You can use lecture notes online, textbook, or other sources. 3) Find one example of inductive reasoning or one example of deductive reasoning in which stereotyping occurs (search the internet, use your own experience/knowledge, or other sources). Describe your example and then describe how the stereotyping results in faulty conjectures or prejudging situations and people. 4) Give an example of a decision that you made recently in which the method of reasoning you used to reach the decision was induction. Describe your reasoning process. RECAP to help you distinguish between inductive and deductive reasoning: Recall what we discussed in class during the first week of classes. Inductive reasoning is the process of arriving at a general conclusion based on observations of specific examples (reasoning from Specific/Particular to General). The conclusion is called a conjecture or a hypothesis. Deductive reasoning is the process of proving a specific conclusion from one or more general statements (reasoning from General to Specific/Particular). -
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I have an internal assessment to do that is crucial for my Math end of year grade. I have gotten a 4/20 on it and I have a chance to correct it. I will send you the feedback that my teacher has sent to me together with the work I have done. Some parts have AI so please paraphrase them and correct them. I need tables and also for you to expand this a lot further by using math in a meaningful manner and not just statistics. You can find more data by searching. The topic has to do with NBA and basketball in general. I believe if you have been watching some basketball it will be more helpful for you to finish this assignment. I will send you the files and the feedback when I select you. Thank you very much!
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Mathematics Question
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mathematics question
Define the function
(
)
=
{
2
sin
?
(
1
2
)
,
0
,
0
,
=
0.
f(x)=
x
2
sin(
x
2
1
),
0,
x
=0,
x=0.
(a)
Prove that
(
)
f(x) is continuous at
=
0
x=0.
(b)
Determine whether
(
)
f(x) is differentiable at
=
0
x=0. If so, find
(
0
)
f
(0).
(c)
Find an explicit formula for
(
)
f
(x) for
0
x
=0.
(d)
Decide whether
(
)
f
(x) is bounded on any neighborhood of
=
0
x=0.
(e)
Determine whether
(
)
f
(x) is Riemann integrable on
[
1
,
1
]
[1,1].
Requirements:
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SKQ-101 Online Sections Graded Homework 3
Graded Question #1: Unit B Exercise 18 Page 93
Write each of the numbers in scientific notation.
a. 3578
b. 984.35
c. 0.0058
d. 624.87
e. 0.0003005
f. 98.180004
Graded Question #2
Compare the numbers in each pair and give the factor by which the numbers differ.
Example:
is
, or 100, times as large as
.
a.
b.
c. 1 million, 1 billion
Graded Question #3: Unit C Exercise 20 Page 106
State the number of significant digits and explain your answer.
350,000 yr
Graded Question #4: Unit C Exercise 22 Page 106
State the number of significant digits and explain your answer.
0.004502 mGraded Question #5: Unit C Exercise 26 Page 106
State the number of significant digits and explain your answer.
mi
Graded Question #6: Unit C Exercise 56 Page 107
Multiply 12 cubic feet by 62.4 lb./cubic foot. Use the appropriate rounding rules to do the
calculation. Express the result with the correct number of significant digits.
Graded Question #7: Unit C Exercise 62 Page 107
Garden mulch costs $46 per cubic yard. How much does it cost to fill your trucks 1.25 cubic yard
cargo area with mulch? Use the appropriate rounding rules to do the calculation. Express the result
with the correct number of significant digits.
referring to the image;
comment on the math assignmentRequirements: Step by Step solution | .doc file
-
mathematics question
Define the function
(
)
=
{
2
sin
?
(
1
2
)
,
0
,
0
,
=
0.
f(x)=
x
2
sin(
x
2
1
),
0,
x
=0,
x=0.
(a)
Prove that
(
)
f(x) is continuous at
=
0
x=0.
(b)
Determine whether
(
)
f(x) is differentiable at
=
0
x=0. If so, find
(
0
)
f
(0).
(c)
Find an explicit formula for
(
)
f
(x) for
0
x
=0.
(d)
Decide whether
(
)
f
(x) is bounded on any neighborhood of
=
0
x=0.
(e)
Determine whether
(
)
f
(x) is Riemann integrable on
[
1
,
1
]
[1,1].
Complete Solution
(a) Continuity at
=
0
x=0
For
0
x
=0,
?
(
)
?
=
?
2
sin
(
1
/
2
)
?
?
2
?
?f(x)?=?x
2
sin(1/x
2
)??x
2
?
Since:
lim
0
2
=
0
x0
lim
x
2
=0
By the Squeeze Theorem:
lim
0
(
)
=
0
=
(
0
)
x0
lim
f(x)=0=f(0)
f is continuous at
0
0.
(b) Differentiability at
=
0
x=0
Using the definition:
(
0
)
=
lim
0
(
)
(
0
)
=
lim
0
2
sin
(
1
/
2
)
=
lim
0
sin
(
1
/
2
)
f
(0)=
h0
lim
h
f(h)f(0)
=
h0
lim
h
h
2
sin(1/h
2
)
=
h0
lim
hsin(1/h
2
)
Since:
1
sin
(
1
/
2
)
1
?
?
sin
(
1
/
2
)
?
?
1sin(1/h
2
)1?h?hsin(1/h
2
)?h?
Thus:
lim
0
sin
(
1
/
2
)
=
0
h0
lim
hsin(1/h
2
)=0
f is differentiable at
0
0, and
(
0
)
=
0
f
(0)=0.
(c) Formula for
(
)
f
(x) for
0
x
=0
Differentiate:
(
)
=
2
sin
(
1
/
2
)
f(x)=x
2
sin(1/x
2
)
Using product and chain rules:
(
)
=
2
sin
(
1
/
2
)
+
2
cos
(
1
/
2
)
(
2
3
)
f
(x)=2xsin(1/x
2
)+x
2
cos(1/x
2
)(
x
3
2
)
Simplifying:
(
)
=
2
sin
(
1
/
2
)
2
cos
(
1
/
2
)
f
(x)=2xsin(1/x
2
)
x
2
cos(1/x
2
)
(d) Boundedness of
(
)
f
(x) near
0
0
Consider:
(
)
=
2
sin
(
1
/
2
)
2
cos
(
1
/
2
)
f
(x)=2xsin(1/x
2
)
x
2
cos(1/x
2
)
The first term
2
sin
(
1
/
2
)
0
2xsin(1/x
2
)0.
The second term:
?
2
cos
(
1
/
2
)
?
=
2
?
?
x
2
cos(1/x
2
)
=
?x?
2
which diverges to infinity as
0
x0.
(
)
f
(x) is unbounded in every neighborhood of
0
0.
(e) Riemann integrability of
(
)
f
(x) on
[
1
,
1
]
[1,1]
Although
(
)
f
(x) is unbounded near
0
0, it is discontinuous only at a single point
=
0
x=0.
A function that is:
bounded on compact intervals except possibly at finitely many points, and
has a finite number of discontinuities,
is Riemann integrable.
Alternatively, note:
1
1
(
)
=
(
1
)
(
1
)
1
1
f
(x)dx=f(1)f(1)
by the Fundamental Theorem of Calculus, since
f is differentiable everywhere and continuous on
[
1
,
1
]
[1,1].
Thus:
(
)
f
(x) is Riemann integrable on
[
1
,
1
]
[1,1].
Requirements:
-
mathematics question
Define the function
(
)
=
{
2
sin
?
(
1
2
)
,
0
,
0
,
=
0.
f(x)=
x
2
sin(
x
2
1
),
0,
x
=0,
x=0.
(a)
Prove that
(
)
f(x) is continuous at
=
0
x=0.
(b)
Determine whether
(
)
f(x) is differentiable at
=
0
x=0. If so, find
(
0
)
f
(0).
(c)
Find an explicit formula for
(
)
f
(x) for
0
x
=0.
(d)
Decide whether
(
)
f
(x) is bounded on any neighborhood of
=
0
x=0.
(e)
Determine whether
(
)
f
(x) is Riemann integrable on
[
1
,
1
]
[1,1].
Requirements:
-
mathematics
Define the function
(
)
=
{
2
sin
?
(
1
2
)
,
0
,
0
,
=
0.
f(x)=
x
2
sin(
x
2
1
),
0,
x
=0,
x=0.
(a)
Prove that
(
)
f(x) is continuous at
=
0
x=0.
(b)
Determine whether
(
)
f(x) is differentiable at
=
0
x=0. If so, find
(
0
)
f
(0).
(c)
Find an explicit formula for
(
)
f
(x) for
0
x
=0.
(d)
Decide whether
(
)
f
(x) is bounded on any neighborhood of
=
0
x=0.
(e)
Determine whether
(
)
f
(x) is Riemann integrable on
[
1
,
1
]
[1,1].
Requirements:
-
mathematics
Define the function
(
)
=
{
2
sin
?
(
1
2
)
,
0
,
0
,
=
0.
f(x)=
x
2
sin(
x
2
1
),
0,
x
=0,
x=0.
(a)
Prove that
(
)
f(x) is continuous at
=
0
x=0.
(b)
Determine whether
(
)
f(x) is differentiable at
=
0
x=0. If so, find
(
0
)
f
(0).
(c)
Find an explicit formula for
(
)
f
(x) for
0
x
=0.
(d)
Decide whether
(
)
f
(x) is bounded on any neighborhood of
=
0
x=0.
(e)
Determine whether
(
)
f
(x) is Riemann integrable on
[
1
,
1
]
[1,1].
Requirements: