i have a math fonction exercice please Help exercice 25

Subhotosh Khan

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i dont know what to do here if someone knows something please help
Please TRANSLATE your assignment into English.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 

lex

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Consider the real-valued function f defined on \(\displaystyle \mathbb{R}\) by:

\(\displaystyle f(x) = x + \frac{1}{\sqrt{1+x^2}}\)


1. Calculate: \(\displaystyle \lim \limits_{x \to +\infty} f(x) \text{ and } \lim \limits_{x \to -\infty} f(x)\)
2. Calculate \(\displaystyle f'(x) \text{ for all } x \in \mathbb{R}\)

1. \(\displaystyle \lim \limits_{x \to +\infty} f(x)\)
As \(\displaystyle x \to +\infty \hspace2ex f(x) = x \hspace1ex+\) a positive term, so \(\displaystyle f(x) \to +\infty\)

\(\displaystyle \lim \limits_{x \to -\infty} f(x)\)
As \(\displaystyle x \to -\infty \hspace2ex f(x) = x\hspace1ex +\) a positive term less than 1, so \(\displaystyle f(x) \to -\infty\)

2. \(\displaystyle f(x) = x + (1+x^2)^{-\tfrac{1}{2}}\)
Hopefully you can differentiate it in this form?
 

nasi112

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Consider the real-valued function f defined on \(\displaystyle \mathbb{R}\) by:

\(\displaystyle f(x) = x + \frac{1}{\sqrt{1+x^2}}\)


1. Calculate: \(\displaystyle \lim \limits_{x \to +\infty} f(x) \text{ and } \lim \limits_{x \to -\infty} f(x)\)
2. Calculate \(\displaystyle f'(x) \text{ for all } x \in \mathbb{R}\)

1. \(\displaystyle \lim \limits_{x \to +\infty} f(x)\)
As \(\displaystyle x \to +\infty \hspace2ex f(x) = x \hspace1ex+\) a positive term, so \(\displaystyle f(x) \to +\infty\)

\(\displaystyle \lim \limits_{x \to -\infty} f(x)\)
As \(\displaystyle x \to -\infty \hspace2ex f(x) = x\hspace1ex +\) a positive term less than 1, so \(\displaystyle f(x) \to -\infty\)

2. \(\displaystyle f(x) = x + (1+x^2)^{-\tfrac{1}{2}}\)
Hopefully you can differentiate it in this form?
since the problem was in French

Salut lex, bienvenue dans le monde des mathématiques françaises

Hi lex, welcome to the world of French mathematics8-)

By the way, you had a beautiful answer above there, but I think that I have seen this question in the forum before. Maybe yesterday. I mean that there are two identical questions from the same OP. And I think that skeeter has answered the first one.
 

lex

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This is clearly a parallel french universe!
Do I take it you are french?
 

Subhotosh Khan

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This is clearly a parallel french universe!
Do I take it you are french?
Like English is second language in India, many ex-colonies of France (Vietnam, Cameroon, Syria, Lebanon, etc.) use French.
 
Last edited:

nasi112

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This is clearly a parallel french universe!
Do I take it you are french?
I studied French. I know some French. I am Bahraini. I don't think that you have ever heard of my country.
 

lex

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I studied French. I know some French. I am Bahraini. I don't think that you have ever heard of my country.
Good Heavens. Yes, I have of course heard of the Bahrain Grand Prix!
Like English is second language in India, many ex-colonies of France (Vietnam, Cameroon, Syria, Lebanon, etc.) use French.
True.
I do like French. I studied it myself many years ago in school. I spent some months in Paris about 15 years ago. Hopefully some day travel will be an option again!
 

nasi112

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Good Heavens. Yes, I have of course heard of the Bahrain Grand Prix!

True.
I do like French. I studied it myself many years ago in school. I spent some months in Paris about 15 years ago. Hopefully some day travel will be an option again!
Yup, Grand Prix, formula 1, is a famous event in Bahrain. And let me guess that you are American or maybe English?
 

lex

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Yup, Grand Prix, formula 1, is a famous event in Bahrain. And let me guess that you are American or maybe English?
Neither. Is Éireannach mé. I am Irish.
 

Jomo

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Please TRANSLATE your assignment into English.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
Come on Subhotosh! Even I could understand the post.
I recall you once posted something in math odds & ends where every word was spelled wrong but everyone understood the post.
I hope that you are enjoying your retirement!
 

jonah2.0

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Beer soaked ramblings follow.
I studied French. I know some French. I am Bahraini. I don't think that you have ever heard of my country.
Bahrain, one of the few countries with no income tax.
I love it.
 
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