Mixing
Limit with three square roots
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I have a task for school to calculate this limit at infinity, I have tried three times but i failed everytime.
$$lim_nrightarrowinftyleft(sqrt4n+1-sqrtn-sqrtn+1right)$$
I know what to do when there are two square roots but when there's three I don't know how to proceed can anyone help me ? Thanks
limits
edited 2 hours ago
cansomeonehelpmeout
5,9273833
asked 2 hours ago
KatarÃna Paľová
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up vote
3
down vote
favorite
I have a task for school to calculate this limit at infinity, I have tried three times but i failed everytime.
$$lim_nrightarrowinftyleft(sqrt4n+1-sqrtn-sqrtn+1right)$$
I know what to do when there are two square roots but when there's three I don't know how to proceed can anyone help me ? Thanks
limits
edited 2 hours ago
cansomeonehelpmeout
5,9273833
asked 2 hours ago
KatarÃna Paľová
161
New contributor
KatarÃna Paľová is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Can you add your working out/thinking to the question? Try and extend your knowledge with 2 to what could happen with 3. You are adding them so the behavior is very similar.
– MRobinson
1 hour ago
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I have a task for school to calculate this limit at infinity, I have tried three times but i failed everytime.
$$lim_nrightarrowinftyleft(sqrt4n+1-sqrtn-sqrtn+1right)$$
I know what to do when there are two square roots but when there's three I don't know how to proceed can anyone help me ? Thanks
limits
edited 2 hours ago
cansomeonehelpmeout
5,9273833
asked 2 hours ago
KatarÃna Paľová
161
New contributor
KatarÃna Paľová is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have a task for school to calculate this limit at infinity, I have tried three times but i failed everytime.
$$lim_nrightarrowinftyleft(sqrt4n+1-sqrtn-sqrtn+1right)$$
I know what to do when there are two square roots but when there's three I don't know how to proceed can anyone help me ? Thanks
limits
limits
edited 2 hours ago
cansomeonehelpmeout
5,9273833
asked 2 hours ago
KatarÃna Paľová
161
New contributor
KatarÃna Paľová is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
cansomeonehelpmeout
5,9273833
asked 2 hours ago
KatarÃna Paľová
161
New contributor
KatarÃna Paľová is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
cansomeonehelpmeout
5,9273833
edited 2 hours ago
cansomeonehelpmeout
5,9273833
edited 2 hours ago
cansomeonehelpmeout
5,9273833
5,9273833
asked 2 hours ago
KatarÃna Paľová
161
New contributor
KatarÃna Paľová is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
KatarÃna Paľová
161
asked 2 hours ago
KatarÃna Paľová
161
161
New contributor
KatarÃna Paľová is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
KatarÃna Paľová is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
KatarÃna Paľová is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Can you add your working out/thinking to the question? Try and extend your knowledge with 2 to what could happen with 3. You are adding them so the behavior is very similar.
– MRobinson
1 hour ago
add a comment |Â
Can you add your working out/thinking to the question? Try and extend your knowledge with 2 to what could happen with 3. You are adding them so the behavior is very similar.
– MRobinson
1 hour ago
Can you add your working out/thinking to the question? Try and extend your knowledge with 2 to what could happen with 3. You are adding them so the behavior is very similar.
– MRobinson
1 hour ago
Can you add your working out/thinking to the question? Try and extend your knowledge with 2 to what could happen with 3. You are adding them so the behavior is very similar.
– MRobinson
1 hour ago
add a comment |Â
4 Answers
4
active
oldest
votes
up vote
4
down vote
Hint: Since you know what to do when there are only two square roots, use the fact that$$(forall ninmathbbN):sqrt4n+1-sqrt n-sqrtn+1=left(sqrtn+frac14-sqrt nright)+left(sqrtn+frac14-sqrtn+1right).$$
answered 2 hours ago
José Carlos Santos
128k17102190
add a comment |Â
up vote
1
down vote
Set $1/n=h^2$
$$lim_hto0^+dfracsqrt4+h^2-1-sqrt1+h^2h$$
$$=lim_...dfracsqrt4+h^2-2h-lim_...dfracsqrt1+h^2-1h=0-0$$ on rationalization of the numerators
answered 1 hour ago
lab bhattacharjee
216k14153267
add a comment |Â
up vote
0
down vote
Write $$frac((sqrt4n+1-sqrtn+1)-sqrtn)((sqrt4n+1-sqrtn+1)+sqrtn)sqrt4n+1-sqrtn+1+sqrtn$$
answered 2 hours ago
Dr. Sonnhard Graubner
69.8k32863
add a comment |Â
up vote
0
down vote
$sqrt4n+1-(sqrtn+sqrtn+1)<sqrt4n+1-2sqrtn=sqrt4n+1-sqrt4n
<frac1sqrt4n+1+sqrt4nto0$
So, the original limit is $0$.
answered 1 hour ago
Yuyi Zhang
132
New contributor
Yuyi Zhang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
Hint: Since you know what to do when there are only two square roots, use the fact that$$(forall ninmathbbN):sqrt4n+1-sqrt n-sqrtn+1=left(sqrtn+frac14-sqrt nright)+left(sqrtn+frac14-sqrtn+1right).$$
answered 2 hours ago
José Carlos Santos
128k17102190
add a comment |Â
up vote
4
down vote
Hint: Since you know what to do when there are only two square roots, use the fact that$$(forall ninmathbbN):sqrt4n+1-sqrt n-sqrtn+1=left(sqrtn+frac14-sqrt nright)+left(sqrtn+frac14-sqrtn+1right).$$
answered 2 hours ago
José Carlos Santos
128k17102190
add a comment |Â
up vote
4
down vote
up vote
4
down vote
Hint: Since you know what to do when there are only two square roots, use the fact that$$(forall ninmathbbN):sqrt4n+1-sqrt n-sqrtn+1=left(sqrtn+frac14-sqrt nright)+left(sqrtn+frac14-sqrtn+1right).$$
answered 2 hours ago
José Carlos Santos
128k17102190
Hint: Since you know what to do when there are only two square roots, use the fact that$$(forall ninmathbbN):sqrt4n+1-sqrt n-sqrtn+1=left(sqrtn+frac14-sqrt nright)+left(sqrtn+frac14-sqrtn+1right).$$
answered 2 hours ago
José Carlos Santos
128k17102190
answered 2 hours ago
José Carlos Santos
128k17102190
answered 2 hours ago
José Carlos Santos
128k17102190
answered 2 hours ago
José Carlos Santos
128k17102190
128k17102190
add a comment |Â
add a comment |Â
up vote
1
down vote
Set $1/n=h^2$
$$lim_hto0^+dfracsqrt4+h^2-1-sqrt1+h^2h$$
$$=lim_...dfracsqrt4+h^2-2h-lim_...dfracsqrt1+h^2-1h=0-0$$ on rationalization of the numerators
answered 1 hour ago
lab bhattacharjee
216k14153267
add a comment |Â
up vote
1
down vote
Set $1/n=h^2$
$$lim_hto0^+dfracsqrt4+h^2-1-sqrt1+h^2h$$
$$=lim_...dfracsqrt4+h^2-2h-lim_...dfracsqrt1+h^2-1h=0-0$$ on rationalization of the numerators
answered 1 hour ago
lab bhattacharjee
216k14153267
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Set $1/n=h^2$
$$lim_hto0^+dfracsqrt4+h^2-1-sqrt1+h^2h$$
$$=lim_...dfracsqrt4+h^2-2h-lim_...dfracsqrt1+h^2-1h=0-0$$ on rationalization of the numerators
answered 1 hour ago
lab bhattacharjee
216k14153267
Set $1/n=h^2$
$$lim_hto0^+dfracsqrt4+h^2-1-sqrt1+h^2h$$
$$=lim_...dfracsqrt4+h^2-2h-lim_...dfracsqrt1+h^2-1h=0-0$$ on rationalization of the numerators
answered 1 hour ago
lab bhattacharjee
216k14153267
answered 1 hour ago
lab bhattacharjee
216k14153267
answered 1 hour ago
lab bhattacharjee
216k14153267
answered 1 hour ago
lab bhattacharjee
216k14153267
216k14153267
add a comment |Â
add a comment |Â
up vote
0
down vote
Write $$frac((sqrt4n+1-sqrtn+1)-sqrtn)((sqrt4n+1-sqrtn+1)+sqrtn)sqrt4n+1-sqrtn+1+sqrtn$$
answered 2 hours ago
Dr. Sonnhard Graubner
69.8k32863
add a comment |Â
up vote
0
down vote
Write $$frac((sqrt4n+1-sqrtn+1)-sqrtn)((sqrt4n+1-sqrtn+1)+sqrtn)sqrt4n+1-sqrtn+1+sqrtn$$
answered 2 hours ago
Dr. Sonnhard Graubner
69.8k32863
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Write $$frac((sqrt4n+1-sqrtn+1)-sqrtn)((sqrt4n+1-sqrtn+1)+sqrtn)sqrt4n+1-sqrtn+1+sqrtn$$
answered 2 hours ago
Dr. Sonnhard Graubner
69.8k32863
Write $$frac((sqrt4n+1-sqrtn+1)-sqrtn)((sqrt4n+1-sqrtn+1)+sqrtn)sqrt4n+1-sqrtn+1+sqrtn$$
answered 2 hours ago
Dr. Sonnhard Graubner
69.8k32863
answered 2 hours ago
Dr. Sonnhard Graubner
69.8k32863
answered 2 hours ago
Dr. Sonnhard Graubner
69.8k32863
answered 2 hours ago
Dr. Sonnhard Graubner
69.8k32863
69.8k32863
add a comment |Â
add a comment |Â
up vote
0
down vote
$sqrt4n+1-(sqrtn+sqrtn+1)<sqrt4n+1-2sqrtn=sqrt4n+1-sqrt4n
<frac1sqrt4n+1+sqrt4nto0$
So, the original limit is $0$.
answered 1 hour ago
Yuyi Zhang
132
New contributor
Yuyi Zhang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
0
down vote
$sqrt4n+1-(sqrtn+sqrtn+1)<sqrt4n+1-2sqrtn=sqrt4n+1-sqrt4n
<frac1sqrt4n+1+sqrt4nto0$
So, the original limit is $0$.
answered 1 hour ago
Yuyi Zhang
132
New contributor
Yuyi Zhang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
0
down vote
up vote
0
down vote
$sqrt4n+1-(sqrtn+sqrtn+1)<sqrt4n+1-2sqrtn=sqrt4n+1-sqrt4n
<frac1sqrt4n+1+sqrt4nto0$
So, the original limit is $0$.
answered 1 hour ago
Yuyi Zhang
132
New contributor
Yuyi Zhang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$sqrt4n+1-(sqrtn+sqrtn+1)<sqrt4n+1-2sqrtn=sqrt4n+1-sqrt4n
<frac1sqrt4n+1+sqrt4nto0$
So, the original limit is $0$.
answered 1 hour ago
Yuyi Zhang
132
New contributor
Yuyi Zhang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 1 hour ago
Yuyi Zhang
132
New contributor
Yuyi Zhang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 1 hour ago
Yuyi Zhang
132
answered 1 hour ago
Yuyi Zhang
132
132
New contributor
Yuyi Zhang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Yuyi Zhang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Yuyi Zhang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
add a comment |Â
KatarÃna Paľová is a new contributor. Be nice, and check out our Code of Conduct.
KatarÃna Paľová is a new contributor. Be nice, and check out our Code of Conduct.
KatarÃna Paľová is a new contributor. Be nice, and check out our Code of Conduct.
KatarÃna Paľová is a new contributor. Be nice, and check out our Code of Conduct.
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Can you add your working out/thinking to the question? Try and extend your knowledge with 2 to what could happen with 3. You are adding them so the behavior is very similar.
– MRobinson
1 hour ago