A Geometrical Visualisation of x1+x<ln(1+x)<x−x22(1+x) for x > 0
In this classroom article, we present a geometrical interpretation of a well-known inequality x 1 + x < l n ( 1 + x ) < x − x 2 2 ( 1 + x ) for x > 0.
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| Published in | Resonance Vol. 23; no. 5; pp. 597 - 600 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New Delhi
Springer India
2018
|
| Subjects | |
| Online Access | Get full text |
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| Abstract | In this classroom article, we present a geometrical interpretation of a well-known inequality
x
1
+
x
<
l
n
(
1
+
x
)
<
x
−
x
2
2
(
1
+
x
)
for
x
> 0. |
|---|---|
| AbstractList | In this classroom article, we present a geometrical interpretation of a well-known inequality
x
1
+
x
<
l
n
(
1
+
x
)
<
x
−
x
2
2
(
1
+
x
)
for
x
> 0. |
| Author | Chakraborty, Sagar |
| Author_xml | – sequence: 1 givenname: Sagar surname: Chakraborty fullname: Chakraborty, Sagar email: sagarchakraborty55@gmail.com organization: Department of Education, University of Kalyani |
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| ContentType | Journal Article |
| Copyright | Indian Academy of Sciences 2018 |
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| DOI | 10.1007/s12045-018-0652-9 |
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| EISSN | 0973-712X |
| EndPage | 600 |
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| Issue | 5 |
| Keywords | logarithm visual proof Inequality |
| Language | English |
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| PublicationYear | 2018 |
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| References | SteinA HMcGavranDA Common LimitCollege Mathematics Journal1998292147 Bikash Chakraborty, Proof Without Words: The Sum of SquaresThe Mathematical Intelligencer2017 NelsenR BProofs Without Words II: More Exercise in Visual ThinkingThe Mathematical Association of America2000 NelsenR BProofs Without Words: Exercise in Visual ThinkingThe Mathematical Association of America1993 |
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| Snippet | In this classroom article, we present a geometrical interpretation of a well-known inequality
x
1
+
x
<
l
n
(
1
+
x
)
<
x
−
x
2
2
(
1
+
x
)
for
x
> 0. |
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| StartPage | 597 |
| SubjectTerms | Classroom Education Humanities and Social Sciences multidisciplinary Science Science Education |
| Title | A Geometrical Visualisation of x1+x<ln(1+x)<x−x22(1+x) for x > 0 |
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