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Hi!

I have some doubts bound up with an exercise of limits. It demands to calculate the existence of the limit in (0,0) of these two functions.

http://www.rinconmatematico.com/latexrender/pictures/bd1b868f7e07af600ea0c82b34a38137.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/5a3966109b20a098800453a99467592c.png [Broken]

My solution for the first one til now is:

http://www.rinconmatematico.com/latexrender/pictures/667c03805a5b4b203406f69cf574c56e.png [Broken]

Well, after the substitution we have http://www.rinconmatematico.com/latexrender/pictures/04dd2173792059a5b0e5447b852baf28.png [Broken]

So we can use http://www.rinconmatematico.com/latexrender/pictures/722e499f2e8ad1b9b66060f151689378.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/2bde7e5f3e31f640f734b26dcf229dc4.png [Broken]

Using http://www.rinconmatematico.com/latexrender/pictures/03d4bbee51cd042a5e43f4b8eed0e81e.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/a4abe4b98d7e1c4782faca7c9db897f9.png [Broken]

And http://www.rinconmatematico.com/latexrender/pictures/597c072a27536c4904c39673dc916ace.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/b04c33391868c0ff16d9fa2933c6466b.png [Broken]

Well, I don't know if I've done correctly all the process, but if I did, I guess that in the next step I have to calculate the limit by the definition to conclude the exercise, and that's one of the things that I don't know how to do.

The second exercise is similar to the first one but I don't know how to do it either. Maybe the minus changes the result and there's not limit and any necessity of employing the definition.

Anyhow, can someone lend me a hand? :)

Thanks!

I have some doubts bound up with an exercise of limits. It demands to calculate the existence of the limit in (0,0) of these two functions.

http://www.rinconmatematico.com/latexrender/pictures/bd1b868f7e07af600ea0c82b34a38137.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/5a3966109b20a098800453a99467592c.png [Broken]

My solution for the first one til now is:

http://www.rinconmatematico.com/latexrender/pictures/667c03805a5b4b203406f69cf574c56e.png [Broken]

Well, after the substitution we have http://www.rinconmatematico.com/latexrender/pictures/04dd2173792059a5b0e5447b852baf28.png [Broken]

So we can use http://www.rinconmatematico.com/latexrender/pictures/722e499f2e8ad1b9b66060f151689378.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/2bde7e5f3e31f640f734b26dcf229dc4.png [Broken]

Using http://www.rinconmatematico.com/latexrender/pictures/03d4bbee51cd042a5e43f4b8eed0e81e.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/a4abe4b98d7e1c4782faca7c9db897f9.png [Broken]

And http://www.rinconmatematico.com/latexrender/pictures/597c072a27536c4904c39673dc916ace.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/b04c33391868c0ff16d9fa2933c6466b.png [Broken]

Well, I don't know if I've done correctly all the process, but if I did, I guess that in the next step I have to calculate the limit by the definition to conclude the exercise, and that's one of the things that I don't know how to do.

The second exercise is similar to the first one but I don't know how to do it either. Maybe the minus changes the result and there's not limit and any necessity of employing the definition.

Anyhow, can someone lend me a hand? :)

Thanks!

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