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Is this a sufficient condition for continuity?
$f(x,y) \to f(x_0,y_0)$, as $x\to x_0, y \to y_0$, imply $\lim_{x,y\to y_0} f(x,y) = f(x_0,y_0)$
Could you explain why this condition is sufficient?
The one that I read is not sufficient,
I could not see the reason behind that.
A:
Not true. The following counterexample is very easy to construct.
Let $f(x,y)=\cos(x)y$. Then
$$\lim_{x\to 0, y\to 0}f(x,y)=0$$
But $\lim_{(x,y)\to(0,0)}f(x,y)=\cos(0)=0$.
If you require continuity in a neighbourhood of $(x_0,y_0)$ then it should work.
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Update: As of Wednesday, Feb. 26, all sites hosting the film A Place in the Sun have been asked to take the film offline and to stop showing trailers and ads for the film. The reason given was the “possible violation of the family’s intellectual property and rights” that was not “legal and completely unfounded,” as the company that posted the trailer is an “independent distributor.”
Original article continues below.
If you thought that you may see A Place in the Sun — the new film from Warren Beatty and Annette Bening — on the big screen this weekend, it looks like that may not be the case. The film is expected to premiere at the Sundance Film Festival, but now that has been cut down to a small slate of theaters.
A source with access to theater lists for AMC movie theaters confirmed to The Hollywood Reporter that A Place in the Sun will only be screening at AMC theaters in the Los Angeles area. While AMC is one of the most well-known theaters for film, most theater chains are now screening the film in smaller cities and are billing it as an indie film.
The film played in a few theaters in the Los Angeles area last weekend, screening the first of two weekly screenings, reports Variety, but it’s unclear if they were screening the film at all other theaters outside of the AMC theaters, except for a select few in Los Angeles. While the movie was only supposed to play in theaters for one more week in order to qualify for the festival, Deadline reports that it will not. A Place in the Sun is a co-production between Sony Pictures Classics and Participant Media, with SPC co-distributing with STXfilms.
The news follows a series of reports that A Place in the Sun is in financial trouble and on the verge of cancellation. Since the film would be earning less money in theaters than in other ways, it is unclear how the film will proceed with its release. The studio, Sony Pictures Entertainment, has an option to buy back the film and release it later in theaters for a small production fee.
A Place in the Sun explores the time the Bens spent working at a big Wall Street firm, their marriage and the two’s recent divorce. It was once set to be
