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Limit of a f(x,y) function

Posted 10 years ago

Hi,

Firstly: Why doesn't this work:

In[88]:= f[x_, y_] = (1/(4*Pi))*Log[(x - 20)^2 + y^2]

Out[88]= Log[(-20 + x)^2]/(4 [Pi])

Secondly: How do I calculate the Limit of a function with two varibales. For example x->20 and y->0

Thirdly, a bit off topic question. Is it really necessary to limit myself to numerical data? For example, instead of number 20 in my expression for f(x,y) I would like to have a constant a. And than calculate Limit x->a and y->0 and also plot the function. Is that possible?

Thank you!

POSTED BY: Mitja Jan?i?
5 Replies
POSTED BY: David Reiss

Well of course you cannot plot (x-a)^2 directly without specifying a value for a since it is not numerical with an arbitrary value of a. You can plot a two-dimensional plot varying both x and a line this:

Plot3D[(x - a)^2, {x, -2, 2}, {a, -1, 1}]

Or you could look at how a plot of (x-a)^2 varies as you change a dynamically using Manipulate, for example:

Manipulate[Plot[(x - a)^2, {x, -2, 2}], {a, -1, 1}]

And, of course, there are many other possibilities...

POSTED BY: David Reiss

In addition to David Reiss' excellent analysis of the issues I will note that, prior to In[88], there was almost certainly something like y=0 executed.

POSTED BY: Daniel Lichtblau

Right! I should never answer these questions before my morning coffee...

POSTED BY: David Reiss

Thanks for your answers, the first two work perfectly, about the third one:

Looks like there was a misunderstanding. Let's say that my function is f(x):=(x-a)^2 where a is an arbitrary constant. Now I want to plot f(x). Is that possible?

POSTED BY: Mitja Jan?i?
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