What is the limit of $frac{sin(5x)}{operatorname{tg}(3x)}$ when $x rightarrow pi$? [closed]
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How to solve this limit without applying L'Hospital's Rule?
calculus
edited Dec 4 at 16:42
Bernard
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asked Dec 4 at 16:00
Edgaras
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closed as off-topic by José Carlos Santos, user302797, Brahadeesh, RRL, Lord_Farin Dec 4 at 17:58
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up vote
-3
down vote
favorite
How to solve this limit without applying L'Hospital's Rule?
calculus
edited Dec 4 at 16:42
Bernard
117k637109
asked Dec 4 at 16:00
Edgaras
1
closed as off-topic by José Carlos Santos, user302797, Brahadeesh, RRL, Lord_Farin Dec 4 at 17:58
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." – José Carlos Santos, user302797, Brahadeesh, RRL, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
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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 4 at 16:00
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up vote
-3
down vote
favorite
up vote
-3
down vote
favorite
How to solve this limit without applying L'Hospital's Rule?
calculus
edited Dec 4 at 16:42
Bernard
117k637109
asked Dec 4 at 16:00
Edgaras
1
How to solve this limit without applying L'Hospital's Rule?
calculus
calculus
edited Dec 4 at 16:42
Bernard
117k637109
asked Dec 4 at 16:00
Edgaras
1
edited Dec 4 at 16:42
Bernard
117k637109
asked Dec 4 at 16:00
Edgaras
1
edited Dec 4 at 16:42
Bernard
117k637109
edited Dec 4 at 16:42
Bernard
117k637109
edited Dec 4 at 16:42
Bernard
117k637109
117k637109
asked Dec 4 at 16:00
Edgaras
1
asked Dec 4 at 16:00
Edgaras
1
asked Dec 4 at 16:00
Edgaras
1
1
closed as off-topic by José Carlos Santos, user302797, Brahadeesh, RRL, Lord_Farin Dec 4 at 17:58
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." – José Carlos Santos, user302797, Brahadeesh, RRL, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by José Carlos Santos, user302797, Brahadeesh, RRL, Lord_Farin Dec 4 at 17:58
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." – José Carlos Santos, user302797, Brahadeesh, RRL, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
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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 4 at 16:00
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1
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 4 at 16:00
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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 4 at 16:00
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.
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Dec 4 at 16:00
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2 Answers
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Hint:
$pi-x=y$
$sin5x=sin5(pi-y)=?$
Now for $yne0$ $$dfrac{sin5y}{tan3y}=dfrac53cdotdfrac{dfrac{sin5y}{5y}}{dfrac{tan3y}{3y}}$$
answered Dec 4 at 16:06
lab bhattacharjee
222k15155273
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Variant, with equivalents:
Near $0$, $;sin usim u$, $; tan usim u$, so
$$frac{sin 5y}{tan 3y}sim_{y=0}frac{5y}{3y}=frac53.$$
answered Dec 4 at 16:45
Bernard
117k637109
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Hint:
$pi-x=y$
$sin5x=sin5(pi-y)=?$
Now for $yne0$ $$dfrac{sin5y}{tan3y}=dfrac53cdotdfrac{dfrac{sin5y}{5y}}{dfrac{tan3y}{3y}}$$
answered Dec 4 at 16:06
lab bhattacharjee
222k15155273
add a comment |
up vote
1
down vote
Hint:
$pi-x=y$
$sin5x=sin5(pi-y)=?$
Now for $yne0$ $$dfrac{sin5y}{tan3y}=dfrac53cdotdfrac{dfrac{sin5y}{5y}}{dfrac{tan3y}{3y}}$$
answered Dec 4 at 16:06
lab bhattacharjee
222k15155273
add a comment |
up vote
1
down vote
up vote
1
down vote
Hint:
$pi-x=y$
$sin5x=sin5(pi-y)=?$
Now for $yne0$ $$dfrac{sin5y}{tan3y}=dfrac53cdotdfrac{dfrac{sin5y}{5y}}{dfrac{tan3y}{3y}}$$
answered Dec 4 at 16:06
lab bhattacharjee
222k15155273
Hint:
$pi-x=y$
$sin5x=sin5(pi-y)=?$
Now for $yne0$ $$dfrac{sin5y}{tan3y}=dfrac53cdotdfrac{dfrac{sin5y}{5y}}{dfrac{tan3y}{3y}}$$
answered Dec 4 at 16:06
lab bhattacharjee
222k15155273
answered Dec 4 at 16:06
lab bhattacharjee
222k15155273
answered Dec 4 at 16:06
lab bhattacharjee
222k15155273
answered Dec 4 at 16:06
lab bhattacharjee
222k15155273
222k15155273
add a comment |
add a comment |
up vote
0
down vote
Variant, with equivalents:
Near $0$, $;sin usim u$, $; tan usim u$, so
$$frac{sin 5y}{tan 3y}sim_{y=0}frac{5y}{3y}=frac53.$$
answered Dec 4 at 16:45
Bernard
117k637109
add a comment |
up vote
0
down vote
Variant, with equivalents:
Near $0$, $;sin usim u$, $; tan usim u$, so
$$frac{sin 5y}{tan 3y}sim_{y=0}frac{5y}{3y}=frac53.$$
answered Dec 4 at 16:45
Bernard
117k637109
add a comment |
up vote
0
down vote
up vote
0
down vote
Variant, with equivalents:
Near $0$, $;sin usim u$, $; tan usim u$, so
$$frac{sin 5y}{tan 3y}sim_{y=0}frac{5y}{3y}=frac53.$$
answered Dec 4 at 16:45
Bernard
117k637109
Variant, with equivalents:
Near $0$, $;sin usim u$, $; tan usim u$, so
$$frac{sin 5y}{tan 3y}sim_{y=0}frac{5y}{3y}=frac53.$$
answered Dec 4 at 16:45
Bernard
117k637109
answered Dec 4 at 16:45
Bernard
117k637109
answered Dec 4 at 16:45
Bernard
117k637109
answered Dec 4 at 16:45
Bernard
117k637109
117k637109
add a comment |
add a comment |
1
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 4 at 16:00