Compute $lim_{xto0} (sin x)^x$ using L'Hospital's rule [closed]

-1

Help me to compute this limit with L'Hospital's rule.

$$lim_{xto 0} (sin x)^x$$

Thanks in advance.

limits

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edited Nov 22 '18 at 11:48

Jean-Claude Arbaut

14.7k63464

asked Nov 22 '18 at 11:40

Rumman Bin Rayhan RijviRumman Bin Rayhan Rijvi

71

closed as off-topic by amWhy, José Carlos Santos, Jean-Claude Arbaut, Nosrati, Hans Lundmark Nov 22 '18 at 20:22

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, José Carlos Santos, Jean-Claude Arbaut, Nosrati, Hans Lundmark

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

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does the limit exist?
  – Akash Roy
  Nov 22 '18 at 11:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  H Hospitals law limits need to solve this math
  – Rumman Bin Rayhan Rijvi
  Nov 22 '18 at 11:43
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  No need to comment on someone's grammar mistakes, especially when English are not they're first language.
  – Rebellos
  Nov 22 '18 at 11:47
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  L. hospitals law
  – Rumman Bin Rayhan Rijvi
  Nov 22 '18 at 11:49
  

  
  
  
  

add a comment | 

-1

Help me to compute this limit with L'Hospital's rule.

$$lim_{xto 0} (sin x)^x$$

Thanks in advance.

limits

share|cite|improve this question

edited Nov 22 '18 at 11:48

Jean-Claude Arbaut

14.7k63464

asked Nov 22 '18 at 11:40

Rumman Bin Rayhan RijviRumman Bin Rayhan Rijvi

71

closed as off-topic by amWhy, José Carlos Santos, Jean-Claude Arbaut, Nosrati, Hans Lundmark Nov 22 '18 at 20:22

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, José Carlos Santos, Jean-Claude Arbaut, Nosrati, Hans Lundmark

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

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does the limit exist?
  – Akash Roy
  Nov 22 '18 at 11:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  H Hospitals law limits need to solve this math
  – Rumman Bin Rayhan Rijvi
  Nov 22 '18 at 11:43
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  No need to comment on someone's grammar mistakes, especially when English are not they're first language.
  – Rebellos
  Nov 22 '18 at 11:47
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  L. hospitals law
  – Rumman Bin Rayhan Rijvi
  Nov 22 '18 at 11:49
  

  
  
  
  

add a comment | 

-1

-1

-1

Help me to compute this limit with L'Hospital's rule.

$$lim_{xto 0} (sin x)^x$$

Thanks in advance.

limits

share|cite|improve this question

edited Nov 22 '18 at 11:48

Jean-Claude Arbaut

14.7k63464

asked Nov 22 '18 at 11:40

Rumman Bin Rayhan RijviRumman Bin Rayhan Rijvi

71

Help me to compute this limit with L'Hospital's rule.

$$lim_{xto 0} (sin x)^x$$

Thanks in advance.

limits

limits

share|cite|improve this question

edited Nov 22 '18 at 11:48

Jean-Claude Arbaut

14.7k63464

asked Nov 22 '18 at 11:40

Rumman Bin Rayhan RijviRumman Bin Rayhan Rijvi

71

share|cite|improve this question

edited Nov 22 '18 at 11:48

Jean-Claude Arbaut

14.7k63464

asked Nov 22 '18 at 11:40

Rumman Bin Rayhan RijviRumman Bin Rayhan Rijvi

71

share|cite|improve this question

share|cite|improve this question

edited Nov 22 '18 at 11:48

Jean-Claude Arbaut

14.7k63464

edited Nov 22 '18 at 11:48

Jean-Claude Arbaut

14.7k63464

edited Nov 22 '18 at 11:48

Jean-Claude Arbaut

14.7k63464

14.7k63464

asked Nov 22 '18 at 11:40

Rumman Bin Rayhan RijviRumman Bin Rayhan Rijvi

71

asked Nov 22 '18 at 11:40

Rumman Bin Rayhan RijviRumman Bin Rayhan Rijvi

71

asked Nov 22 '18 at 11:40

Rumman Bin Rayhan RijviRumman Bin Rayhan Rijvi

71

71

closed as off-topic by amWhy, José Carlos Santos, Jean-Claude Arbaut, Nosrati, Hans Lundmark Nov 22 '18 at 20:22

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, José Carlos Santos, Jean-Claude Arbaut, Nosrati, Hans Lundmark

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

closed as off-topic by amWhy, José Carlos Santos, Jean-Claude Arbaut, Nosrati, Hans Lundmark Nov 22 '18 at 20:22

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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, José Carlos Santos, Jean-Claude Arbaut, Nosrati, Hans Lundmark

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

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does the limit exist?
  – Akash Roy
  Nov 22 '18 at 11:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  H Hospitals law limits need to solve this math
  – Rumman Bin Rayhan Rijvi
  Nov 22 '18 at 11:43
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  No need to comment on someone's grammar mistakes, especially when English are not they're first language.
  – Rebellos
  Nov 22 '18 at 11:47
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  L. hospitals law
  – Rumman Bin Rayhan Rijvi
  Nov 22 '18 at 11:49
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does the limit exist?
  – Akash Roy
  Nov 22 '18 at 11:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  H Hospitals law limits need to solve this math
  – Rumman Bin Rayhan Rijvi
  Nov 22 '18 at 11:43
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  No need to comment on someone's grammar mistakes, especially when English are not they're first language.
  – Rebellos
  Nov 22 '18 at 11:47
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  L. hospitals law
  – Rumman Bin Rayhan Rijvi
  Nov 22 '18 at 11:49
  

  
  
  
  

Does the limit exist?
– Akash Roy
Nov 22 '18 at 11:42

Does the limit exist?
– Akash Roy
Nov 22 '18 at 11:42

H Hospitals law limits need to solve this math
– Rumman Bin Rayhan Rijvi
Nov 22 '18 at 11:43

H Hospitals law limits need to solve this math
– Rumman Bin Rayhan Rijvi
Nov 22 '18 at 11:43

4

4

No need to comment on someone's grammar mistakes, especially when English are not they're first language.
– Rebellos
Nov 22 '18 at 11:47

No need to comment on someone's grammar mistakes, especially when English are not they're first language.
– Rebellos
Nov 22 '18 at 11:47

L. hospitals law
– Rumman Bin Rayhan Rijvi
Nov 22 '18 at 11:49

L. hospitals law
– Rumman Bin Rayhan Rijvi
Nov 22 '18 at 11:49

add a comment | 

2 Answers
2

active

oldest

votes

2

HINT

We need $x>0$, then use

$$ (sin x)^x=e^{x log sin x}=e^{frac{log sin x}{frac1x}}$$

share|cite|improve this answer

answered Nov 22 '18 at 11:47

gimusigimusi

1

add a comment | 

1

Use L'Hospital's rule to complete the standard exercise of finding that
$$ lim_{xto0}frac{sin x}{x}=1.$$
So we have that, as $xto0$, $sin xsim x$. Now the limit you have becomes
$$L=lim_{xto0}(sin x)^x = lim_{xto 0}x^x = lim_{xto0}e^{xln x}.$$
Now, take the log of this limit and find $ln L$. Once you've done that, just exponentiate this value to find $L$.

share|cite|improve this answer

answered Nov 22 '18 at 12:22

YiFanYiFan

2,6941422

add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

2

HINT

We need $x>0$, then use

$$ (sin x)^x=e^{x log sin x}=e^{frac{log sin x}{frac1x}}$$

share|cite|improve this answer

answered Nov 22 '18 at 11:47

gimusigimusi

1

add a comment | 

2

HINT

We need $x>0$, then use

$$ (sin x)^x=e^{x log sin x}=e^{frac{log sin x}{frac1x}}$$

share|cite|improve this answer

answered Nov 22 '18 at 11:47

gimusigimusi

1

add a comment | 

2

2

2

HINT

We need $x>0$, then use

$$ (sin x)^x=e^{x log sin x}=e^{frac{log sin x}{frac1x}}$$

share|cite|improve this answer

answered Nov 22 '18 at 11:47

gimusigimusi

1

HINT

We need $x>0$, then use

$$ (sin x)^x=e^{x log sin x}=e^{frac{log sin x}{frac1x}}$$

share|cite|improve this answer

answered Nov 22 '18 at 11:47

gimusigimusi

1

share|cite|improve this answer

share|cite|improve this answer

answered Nov 22 '18 at 11:47

gimusigimusi

1

answered Nov 22 '18 at 11:47

gimusigimusi

1

answered Nov 22 '18 at 11:47

gimusigimusi

1

1

add a comment | 

add a comment | 

1

Use L'Hospital's rule to complete the standard exercise of finding that
$$ lim_{xto0}frac{sin x}{x}=1.$$
So we have that, as $xto0$, $sin xsim x$. Now the limit you have becomes
$$L=lim_{xto0}(sin x)^x = lim_{xto 0}x^x = lim_{xto0}e^{xln x}.$$
Now, take the log of this limit and find $ln L$. Once you've done that, just exponentiate this value to find $L$.

share|cite|improve this answer

answered Nov 22 '18 at 12:22

YiFanYiFan

2,6941422

add a comment | 

1

Use L'Hospital's rule to complete the standard exercise of finding that
$$ lim_{xto0}frac{sin x}{x}=1.$$
So we have that, as $xto0$, $sin xsim x$. Now the limit you have becomes
$$L=lim_{xto0}(sin x)^x = lim_{xto 0}x^x = lim_{xto0}e^{xln x}.$$
Now, take the log of this limit and find $ln L$. Once you've done that, just exponentiate this value to find $L$.

share|cite|improve this answer

answered Nov 22 '18 at 12:22

YiFanYiFan

2,6941422

add a comment | 

1

1

1

Use L'Hospital's rule to complete the standard exercise of finding that
$$ lim_{xto0}frac{sin x}{x}=1.$$
So we have that, as $xto0$, $sin xsim x$. Now the limit you have becomes
$$L=lim_{xto0}(sin x)^x = lim_{xto 0}x^x = lim_{xto0}e^{xln x}.$$
Now, take the log of this limit and find $ln L$. Once you've done that, just exponentiate this value to find $L$.

share|cite|improve this answer

answered Nov 22 '18 at 12:22

YiFanYiFan

2,6941422

Use L'Hospital's rule to complete the standard exercise of finding that
$$ lim_{xto0}frac{sin x}{x}=1.$$
So we have that, as $xto0$, $sin xsim x$. Now the limit you have becomes
$$L=lim_{xto0}(sin x)^x = lim_{xto 0}x^x = lim_{xto0}e^{xln x}.$$
Now, take the log of this limit and find $ln L$. Once you've done that, just exponentiate this value to find $L$.

share|cite|improve this answer

answered Nov 22 '18 at 12:22

YiFanYiFan

2,6941422

share|cite|improve this answer

share|cite|improve this answer

answered Nov 22 '18 at 12:22

YiFanYiFan

2,6941422

answered Nov 22 '18 at 12:22

YiFanYiFan

2,6941422

answered Nov 22 '18 at 12:22

YiFanYiFan

2,6941422

2,6941422

add a comment | 

add a comment | 

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