How to prove that this limit does not exist? $lim _ (x,y) rightarrow (0,0) frac2yx^2 + y^2 cos frac1x^2 + y^2$ [on hold] The Next CEO of Stack OverflowSomething is wrong with this proof, limit $limlimits_(x,y) to (0,0) fracxy^3x^4 + 3y^4$Please explain me how can I show that the last limit does not exist?To prove the limit of given function does not exist.Prove that $lim_(x,y)rightarrow(0,0) fracx^c + $ does not existHow to show that $lim_(x,y)rightarrow (0,0) 2^fracxyx^2+3y^2$ does not exist?How to show that $lim_(x,y)to(0,0)fracxy^2x^2+y^3$ does not exist?How does one prove $limlimits_n→+∞ fracsin(n+1)sin(n)$ does not exist by means of contradiction?how to show limit of $fracx^2-y^2x^3-y^3$ as (x,y) goes to $(0,0)$ does not existFor each of the following evaluate the limit or show that the limit does not exist $lim_(x, y) to (0,0) fracsin(x-y)$$ lim_(x,y)rightarrow (0,0) fracx^5y^3x^6+y^4. $ Does it exist or not?
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How to prove that this limit does not exist? $lim _ (x,y) rightarrow (0,0) frac2yx^2 + y^2 cos frac1x^2 + y^2$ [on hold]
The Next CEO of Stack OverflowSomething is wrong with this proof, limit $limlimits_(x,y) to (0,0) fracxy^3x^4 + 3y^4$Please explain me how can I show that the last limit does not exist?To prove the limit of given function does not exist.Prove that $lim_(x,y)rightarrow(0,0) frac^ax$ does not existHow to show that $lim_(x,y)rightarrow (0,0) 2^fracxyx^2+3y^2$ does not exist?How to show that $lim_(x,y)to(0,0)fracxy^2x^2+y^3$ does not exist?How does one prove $limlimits_n→+∞ fracsin(n+1)sin(n)$ does not exist by means of contradiction?how to show limit of $fracx^2-y^2x^3-y^3$ as (x,y) goes to $(0,0)$ does not existFor each of the following evaluate the limit or show that the limit does not exist $lim_(x, y) to (0,0) fracsin(x-y)$$ lim_(x,y)rightarrow (0,0) fracx^5y^3x^6+y^4. $ Does it exist or not?
$begingroup$
How can I show that this limit does not exist:
$$lim _ (x,y) rightarrow (0,0) frac2yx^2 + y^2 cos frac1x^2 + y^2;?$$
I am confused because we have 2 variables. Could anyone help me please?
calculus sequences-and-series limits multivariable-calculus
edited Mar 28 at 4:51
Blue
49.3k870157
asked Mar 28 at 1:38
hopefullyhopefully
301214
$endgroup$
put on hold as off-topic by Saad, RRL, Delta-u, YiFan, José Carlos Santos Mar 28 at 13:52
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." – Saad, RRL, Delta-u, YiFan, José Carlos Santos
|
show 1 more comment
$begingroup$
How can I show that this limit does not exist:
$$lim _ (x,y) rightarrow (0,0) frac2yx^2 + y^2 cos frac1x^2 + y^2;?$$
I am confused because we have 2 variables. Could anyone help me please?
calculus sequences-and-series limits multivariable-calculus
edited Mar 28 at 4:51
Blue
49.3k870157
asked Mar 28 at 1:38
hopefullyhopefully
301214
$endgroup$
put on hold as off-topic by Saad, RRL, Delta-u, YiFan, José Carlos Santos Mar 28 at 13:52
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." – Saad, RRL, Delta-u, YiFan, José Carlos Santos
$begingroup$
You want to prove that a limit does not exist and ask in the title how to prove differentiability? This does not go together.
$endgroup$
– amsmath
Mar 28 at 1:40
$begingroup$
I am sorry I have fixed this error @amsmath
$endgroup$
– hopefully
Mar 28 at 1:41
$begingroup$
If you are "confused because we have 2 variables", you should be looking at much much much easier 2-variable problems, and coming back to this one later.
$endgroup$
– David
Mar 28 at 1:42
2
$begingroup$
Let $y = x$ to get an idea.
$endgroup$
– amsmath
Mar 28 at 1:43
1
$begingroup$
I have already let y=x=1/n ... and then substituted for $n = sqrt pi$ one time and $sqrt2 pi$ the other time .... this is why I know that the limit DNE ..... I only do not know how to write it @amsmath
$endgroup$
– hopefully
Mar 28 at 1:46
|
show 1 more comment
$begingroup$
How can I show that this limit does not exist:
$$lim _ (x,y) rightarrow (0,0) frac2yx^2 + y^2 cos frac1x^2 + y^2;?$$
I am confused because we have 2 variables. Could anyone help me please?
calculus sequences-and-series limits multivariable-calculus
edited Mar 28 at 4:51
Blue
49.3k870157
asked Mar 28 at 1:38
hopefullyhopefully
301214
$endgroup$
How can I show that this limit does not exist:
$$lim _ (x,y) rightarrow (0,0) frac2yx^2 + y^2 cos frac1x^2 + y^2;?$$
I am confused because we have 2 variables. Could anyone help me please?
calculus sequences-and-series limits multivariable-calculus
calculus sequences-and-series limits multivariable-calculus
edited Mar 28 at 4:51
Blue
49.3k870157
asked Mar 28 at 1:38
hopefullyhopefully
301214
edited Mar 28 at 4:51
Blue
49.3k870157
asked Mar 28 at 1:38
hopefullyhopefully
301214
edited Mar 28 at 4:51
Blue
49.3k870157
edited Mar 28 at 4:51
Blue
49.3k870157
edited Mar 28 at 4:51
Blue
49.3k870157
49.3k870157
asked Mar 28 at 1:38
hopefullyhopefully
301214
asked Mar 28 at 1:38
hopefullyhopefully
301214
asked Mar 28 at 1:38
hopefullyhopefully
301214
301214
put on hold as off-topic by Saad, RRL, Delta-u, YiFan, José Carlos Santos Mar 28 at 13:52
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." – Saad, RRL, Delta-u, YiFan, José Carlos Santos
put on hold as off-topic by Saad, RRL, Delta-u, YiFan, José Carlos Santos Mar 28 at 13:52
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." – Saad, RRL, Delta-u, YiFan, José Carlos Santos
$begingroup$
You want to prove that a limit does not exist and ask in the title how to prove differentiability? This does not go together.
$endgroup$
– amsmath
Mar 28 at 1:40
$begingroup$
I am sorry I have fixed this error @amsmath
$endgroup$
– hopefully
Mar 28 at 1:41
$begingroup$
If you are "confused because we have 2 variables", you should be looking at much much much easier 2-variable problems, and coming back to this one later.
$endgroup$
– David
Mar 28 at 1:42
2
$begingroup$
Let $y = x$ to get an idea.
$endgroup$
– amsmath
Mar 28 at 1:43
1
$begingroup$
I have already let y=x=1/n ... and then substituted for $n = sqrt pi$ one time and $sqrt2 pi$ the other time .... this is why I know that the limit DNE ..... I only do not know how to write it @amsmath
$endgroup$
– hopefully
Mar 28 at 1:46
|
show 1 more comment
$begingroup$
You want to prove that a limit does not exist and ask in the title how to prove differentiability? This does not go together.
$endgroup$
– amsmath
Mar 28 at 1:40
$begingroup$
I am sorry I have fixed this error @amsmath
$endgroup$
– hopefully
Mar 28 at 1:41
$begingroup$
If you are "confused because we have 2 variables", you should be looking at much much much easier 2-variable problems, and coming back to this one later.
$endgroup$
– David
Mar 28 at 1:42
2
$begingroup$
Let $y = x$ to get an idea.
$endgroup$
– amsmath
Mar 28 at 1:43
1
$begingroup$
I have already let y=x=1/n ... and then substituted for $n = sqrt pi$ one time and $sqrt2 pi$ the other time .... this is why I know that the limit DNE ..... I only do not know how to write it @amsmath
$endgroup$
– hopefully
Mar 28 at 1:46
$begingroup$
You want to prove that a limit does not exist and ask in the title how to prove differentiability? This does not go together.
$endgroup$
– amsmath
Mar 28 at 1:40
$begingroup$
You want to prove that a limit does not exist and ask in the title how to prove differentiability? This does not go together.
$endgroup$
– amsmath
Mar 28 at 1:40
$begingroup$
I am sorry I have fixed this error @amsmath
$endgroup$
– hopefully
Mar 28 at 1:41
$begingroup$
I am sorry I have fixed this error @amsmath
$endgroup$
– hopefully
Mar 28 at 1:41
$begingroup$
If you are "confused because we have 2 variables", you should be looking at much much much easier 2-variable problems, and coming back to this one later.
$endgroup$
– David
Mar 28 at 1:42
$begingroup$
If you are "confused because we have 2 variables", you should be looking at much much much easier 2-variable problems, and coming back to this one later.
$endgroup$
– David
Mar 28 at 1:42
2
2
$begingroup$
Let $y = x$ to get an idea.
$endgroup$
– amsmath
Mar 28 at 1:43
$begingroup$
Let $y = x$ to get an idea.
$endgroup$
– amsmath
Mar 28 at 1:43
1
1
$begingroup$
I have already let y=x=1/n ... and then substituted for $n = sqrt pi$ one time and $sqrt2 pi$ the other time .... this is why I know that the limit DNE ..... I only do not know how to write it @amsmath
$endgroup$
– hopefully
Mar 28 at 1:46
$begingroup$
I have already let y=x=1/n ... and then substituted for $n = sqrt pi$ one time and $sqrt2 pi$ the other time .... this is why I know that the limit DNE ..... I only do not know how to write it @amsmath
$endgroup$
– hopefully
Mar 28 at 1:46
|
show 1 more comment
2 Answers
2
active
oldest
votes
$begingroup$
For the limit to exist, the limit value should be same when you approach to the origin from every direction. (It's like that the limit should be same from the left and from the right for one-dimensional limits.)
Let $(x,y)=(rcostheta,rsintheta)$. Then your formula becomes:
$$lim_rto0frac2sinthetarcosleft(frac1r^2right)$$
You can see that the limit is D.N.E. when $sinthetane0$, and it is zero when $sintheta=0$. So the limit does not exist.
answered Mar 28 at 4:45
Kay K.Kay K.
6,9401337
$endgroup$
add a comment |
$begingroup$
Put $x=0$ and $y=frac 1 sqrt 2n pi$. Write down $f(x,y)$ and observe that this tends to $infty$ as $ n to infty$.
answered Mar 28 at 6:34
Kavi Rama MurthyKavi Rama Murthy
71.3k53170
$endgroup$
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
For the limit to exist, the limit value should be same when you approach to the origin from every direction. (It's like that the limit should be same from the left and from the right for one-dimensional limits.)
Let $(x,y)=(rcostheta,rsintheta)$. Then your formula becomes:
$$lim_rto0frac2sinthetarcosleft(frac1r^2right)$$
You can see that the limit is D.N.E. when $sinthetane0$, and it is zero when $sintheta=0$. So the limit does not exist.
answered Mar 28 at 4:45
Kay K.Kay K.
6,9401337
$endgroup$
add a comment |
$begingroup$
For the limit to exist, the limit value should be same when you approach to the origin from every direction. (It's like that the limit should be same from the left and from the right for one-dimensional limits.)
Let $(x,y)=(rcostheta,rsintheta)$. Then your formula becomes:
$$lim_rto0frac2sinthetarcosleft(frac1r^2right)$$
You can see that the limit is D.N.E. when $sinthetane0$, and it is zero when $sintheta=0$. So the limit does not exist.
answered Mar 28 at 4:45
Kay K.Kay K.
6,9401337
$endgroup$
add a comment |
$begingroup$
For the limit to exist, the limit value should be same when you approach to the origin from every direction. (It's like that the limit should be same from the left and from the right for one-dimensional limits.)
Let $(x,y)=(rcostheta,rsintheta)$. Then your formula becomes:
$$lim_rto0frac2sinthetarcosleft(frac1r^2right)$$
You can see that the limit is D.N.E. when $sinthetane0$, and it is zero when $sintheta=0$. So the limit does not exist.
answered Mar 28 at 4:45
Kay K.Kay K.
6,9401337
$endgroup$
For the limit to exist, the limit value should be same when you approach to the origin from every direction. (It's like that the limit should be same from the left and from the right for one-dimensional limits.)
Let $(x,y)=(rcostheta,rsintheta)$. Then your formula becomes:
$$lim_rto0frac2sinthetarcosleft(frac1r^2right)$$
You can see that the limit is D.N.E. when $sinthetane0$, and it is zero when $sintheta=0$. So the limit does not exist.
answered Mar 28 at 4:45
Kay K.Kay K.
6,9401337
answered Mar 28 at 4:45
Kay K.Kay K.
6,9401337
answered Mar 28 at 4:45
Kay K.Kay K.
6,9401337
answered Mar 28 at 4:45
Kay K.Kay K.
6,9401337
6,9401337
add a comment |
add a comment |
$begingroup$
Put $x=0$ and $y=frac 1 sqrt 2n pi$. Write down $f(x,y)$ and observe that this tends to $infty$ as $ n to infty$.
answered Mar 28 at 6:34
Kavi Rama MurthyKavi Rama Murthy
71.3k53170
$endgroup$
add a comment |
$begingroup$
Put $x=0$ and $y=frac 1 sqrt 2n pi$. Write down $f(x,y)$ and observe that this tends to $infty$ as $ n to infty$.
answered Mar 28 at 6:34
Kavi Rama MurthyKavi Rama Murthy
71.3k53170
$endgroup$
add a comment |
$begingroup$
Put $x=0$ and $y=frac 1 sqrt 2n pi$. Write down $f(x,y)$ and observe that this tends to $infty$ as $ n to infty$.
answered Mar 28 at 6:34
Kavi Rama MurthyKavi Rama Murthy
71.3k53170
$endgroup$
Put $x=0$ and $y=frac 1 sqrt 2n pi$. Write down $f(x,y)$ and observe that this tends to $infty$ as $ n to infty$.
answered Mar 28 at 6:34
Kavi Rama MurthyKavi Rama Murthy
71.3k53170
answered Mar 28 at 6:34
Kavi Rama MurthyKavi Rama Murthy
71.3k53170
answered Mar 28 at 6:34
Kavi Rama MurthyKavi Rama Murthy
71.3k53170
answered Mar 28 at 6:34
Kavi Rama MurthyKavi Rama Murthy
71.3k53170
71.3k53170
add a comment |
add a comment |
$begingroup$
You want to prove that a limit does not exist and ask in the title how to prove differentiability? This does not go together.
$endgroup$
– amsmath
Mar 28 at 1:40
$begingroup$
I am sorry I have fixed this error @amsmath
$endgroup$
– hopefully
Mar 28 at 1:41
$begingroup$
If you are "confused because we have 2 variables", you should be looking at much much much easier 2-variable problems, and coming back to this one later.
$endgroup$
– David
Mar 28 at 1:42
2
$begingroup$
Let $y = x$ to get an idea.
$endgroup$
– amsmath
Mar 28 at 1:43
1
$begingroup$
I have already let y=x=1/n ... and then substituted for $n = sqrt pi$ one time and $sqrt2 pi$ the other time .... this is why I know that the limit DNE ..... I only do not know how to write it @amsmath
$endgroup$
– hopefully
Mar 28 at 1:46