I am learning continuous function, please help me. Show that the following function is continuous everywhere: $\vec{F}(x_1,x_2)=x_1\sin{\left(\frac{1}{x_2}\right)}+x_2\sin{\left(\frac{1}{x_1}\right)}$ if $x_1x_2\neq 0$ and $\vec{F}(x_1,x_2)=0$ if $x_1x_2 = 0$
Show the function $x_1\sin(1/x_2)+x_2\sin(1/x_1)$ is continuous everywhere
2
$\begingroup$
multivariable-calculus
continuity
-
1What do you know about a) the composition of continuous functions; b) the definition of continuity? – 2012-12-17
-
0@Coga81: Do you mean $F(x_1, x_2)$ instead of $F(u, v)$? Also, why do you have an arrow over $F$? – 2012-12-17
-
0Thank you very much, I am preparing basis for differential geometry. That why I wrote an arrow over F (vector function). It is written exactly from my book. – 2012-12-17
-
0It's unusual to call this function $\vec{F}$ rather than $F$, since there is only one output variable. It makes me wonder if there has not been a typo or transcription error somewhere. – 2014-08-08