Edit
I just realized that I don't have to worry about this; the worksheet says "Find the value of the limit using Mathematica or justify the limit does not exist". I've already done so by hand, so me asking this is probably pointless.
Thank you to everyone who gave answers, and sorry for wasting your time.
Welp. I can't find anything helpful, so here we go again.
I'm trying to find the multivariable limit (if it exists) of
$$\lim_{(x,y)\to(0,0)}\frac{2x+y} {x+3y}$$
Mathematica says that the limit evaluates to $2$, but I ran it through manually along the x- and y-axes and got that the limit does not exist. Wolfram Alpha agrees with my result.
$f(x,0) = 2; f(0,y) = \frac{1}{3}; 2 \ne \frac{1}{3}$
I have no idea why Mathematica got the result it did or how to fix it, if possible. This was done in Mathematica 11.0, if that makes any difference.
The input and output is as follows:
In:= w[x_, y_] = (2*x + y)/(x + 3*y)
Out= (2*x + y)/(x + 3*y)
In:= Limit[Limit[w[x, y], y -> 0], x -> 0]
Out= 2
By hand:
Along y=0 (x-axis): $f(x,0) = \frac{2x}{x} = 2$
Along x=0: $f(0,y) = \frac{y}{3y} = \frac{1}{3}$
$2 \ne \frac{1}{3}$ so limit does not exist
x
and is in fact2
for all nonzerox
. So if the limit exists, it has to be2
. Perhaps the links to the related problems can help you get Mathematica to prove or disprove that it is2
. $\endgroup$