Help with a limit (without L'Hopital): $lim_{xto 0^+} x^{sin x}$ [closed]

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What is the limit?
$$lim_{xto 0^+} x^{sin x }$$

edited Dec 27 '18 at 10:49

Blue

47.6k870151

asked Dec 27 '18 at 9:24

Amit Yeffet

New contributor

closed as off-topic by Henrik, Eevee Trainer, Shaun, Davide Giraudo, Saad Dec 27 '18 at 12:08

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Henrik, Eevee Trainer, Shaun, Davide Giraudo, Saad

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Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 27 '18 at 9:28

Here's a MathJax tutorial :)
– Shaun
Dec 27 '18 at 9:41

add a comment |

-3

What is the limit?
$$lim_{xto 0^+} x^{sin x }$$

edited Dec 27 '18 at 10:49

Blue

47.6k870151

asked Dec 27 '18 at 9:24

Amit Yeffet

New contributor

closed as off-topic by Henrik, Eevee Trainer, Shaun, Davide Giraudo, Saad Dec 27 '18 at 12:08

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Henrik, Eevee Trainer, Shaun, Davide Giraudo, Saad

If this question can be reworded to fit the rules in the help center, please edit the question.

Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 27 '18 at 9:28

Here's a MathJax tutorial :)
– Shaun
Dec 27 '18 at 9:41

add a comment |

-3

What is the limit?
$$lim_{xto 0^+} x^{sin x }$$

edited Dec 27 '18 at 10:49

Blue

47.6k870151

asked Dec 27 '18 at 9:24

Amit Yeffet

New contributor

What is the limit?
$$lim_{xto 0^+} x^{sin x }$$

calculus limits trigonometry limits-without-lhopital

edited Dec 27 '18 at 10:49

Blue

47.6k870151

asked Dec 27 '18 at 9:24

Amit Yeffet

New contributor

edited Dec 27 '18 at 10:49

Blue

47.6k870151

asked Dec 27 '18 at 9:24

Amit Yeffet

New contributor

edited Dec 27 '18 at 10:49

Blue

47.6k870151

edited Dec 27 '18 at 10:49

Blue

47.6k870151

edited Dec 27 '18 at 10:49

Blue

47.6k870151

asked Dec 27 '18 at 9:24

Amit Yeffet

New contributor

asked Dec 27 '18 at 9:24

Amit Yeffet

asked Dec 27 '18 at 9:24

Amit Yeffet

New contributor

Amit Yeffet is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

closed as off-topic by Henrik, Eevee Trainer, Shaun, Davide Giraudo, Saad Dec 27 '18 at 12:08

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Henrik, Eevee Trainer, Shaun, Davide Giraudo, Saad

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Henrik, Eevee Trainer, Shaun, Davide Giraudo, Saad Dec 27 '18 at 12:08

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Henrik, Eevee Trainer, Shaun, Davide Giraudo, Saad

If this question can be reworded to fit the rules in the help center, please edit the question.

Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 27 '18 at 9:28

Here's a MathJax tutorial :)
– Shaun
Dec 27 '18 at 9:41

add a comment |

Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 27 '18 at 9:28

Here's a MathJax tutorial :)
– Shaun
Dec 27 '18 at 9:41

Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Dec 27 '18 at 9:28

Here's a MathJax tutorial :)
– Shaun
Dec 27 '18 at 9:41

add a comment |

2 Answers
2

active

oldest

votes

Rewrite as
$$
x^{sin x}=e^{sin xlog x}=e^{frac{sin x}{x}(xlog x)}
$$
and using $sin x/xto 1$ and $xlog xto 0$, the limit is $e^0=1$.

answered Dec 27 '18 at 9:28

Pierpaolo Vivo

5,3962624

add a comment |

Hint: Use the expansion for $sin x$.

$$sin x = x-frac{x^3}{3!}+frac{x^5}{5!}-…$$

Apply this to

$$x^{sin x}$$

and let $x to 0^+$. Also, note that

$$lim_{ x to 0^+} x^x = 1$$

edited Dec 27 '18 at 9:33

answered Dec 27 '18 at 9:28

KM101

5,0391423

add a comment |

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

Rewrite as
$$
x^{sin x}=e^{sin xlog x}=e^{frac{sin x}{x}(xlog x)}
$$
and using $sin x/xto 1$ and $xlog xto 0$, the limit is $e^0=1$.

answered Dec 27 '18 at 9:28

Pierpaolo Vivo

5,3962624

add a comment |

Rewrite as
$$
x^{sin x}=e^{sin xlog x}=e^{frac{sin x}{x}(xlog x)}
$$
and using $sin x/xto 1$ and $xlog xto 0$, the limit is $e^0=1$.

answered Dec 27 '18 at 9:28

Pierpaolo Vivo

5,3962624

add a comment |

Rewrite as
$$
x^{sin x}=e^{sin xlog x}=e^{frac{sin x}{x}(xlog x)}
$$
and using $sin x/xto 1$ and $xlog xto 0$, the limit is $e^0=1$.

answered Dec 27 '18 at 9:28

Pierpaolo Vivo

5,3962624

Rewrite as
$$
x^{sin x}=e^{sin xlog x}=e^{frac{sin x}{x}(xlog x)}
$$
and using $sin x/xto 1$ and $xlog xto 0$, the limit is $e^0=1$.

answered Dec 27 '18 at 9:28

Pierpaolo Vivo

5,3962624

answered Dec 27 '18 at 9:28

Pierpaolo Vivo

5,3962624

answered Dec 27 '18 at 9:28

Pierpaolo Vivo

5,3962624

answered Dec 27 '18 at 9:28

Pierpaolo Vivo

5,3962624

add a comment |

Hint: Use the expansion for $sin x$.

$$sin x = x-frac{x^3}{3!}+frac{x^5}{5!}-…$$

Apply this to

$$x^{sin x}$$

and let $x to 0^+$. Also, note that

$$lim_{ x to 0^+} x^x = 1$$

edited Dec 27 '18 at 9:33

answered Dec 27 '18 at 9:28

KM101

5,0391423

add a comment |

Hint: Use the expansion for $sin x$.

$$sin x = x-frac{x^3}{3!}+frac{x^5}{5!}-…$$

Apply this to

$$x^{sin x}$$

and let $x to 0^+$. Also, note that

$$lim_{ x to 0^+} x^x = 1$$

edited Dec 27 '18 at 9:33

answered Dec 27 '18 at 9:28

KM101

5,0391423

add a comment |

Hint: Use the expansion for $sin x$.

$$sin x = x-frac{x^3}{3!}+frac{x^5}{5!}-…$$

Apply this to

$$x^{sin x}$$

and let $x to 0^+$. Also, note that

$$lim_{ x to 0^+} x^x = 1$$

edited Dec 27 '18 at 9:33

answered Dec 27 '18 at 9:28

KM101

5,0391423

Hint: Use the expansion for $sin x$.

$$sin x = x-frac{x^3}{3!}+frac{x^5}{5!}-…$$

Apply this to

$$x^{sin x}$$

and let $x to 0^+$. Also, note that

$$lim_{ x to 0^+} x^x = 1$$

edited Dec 27 '18 at 9:33

answered Dec 27 '18 at 9:28

KM101

5,0391423

edited Dec 27 '18 at 9:33

answered Dec 27 '18 at 9:28

KM101

5,0391423

answered Dec 27 '18 at 9:28

KM101

5,0391423

answered Dec 27 '18 at 9:28

KM101

5,0391423

add a comment |

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