How to find a function in a piecewise function

Questions
1

Is there a way to find the function “L” in this piecewise function, for the function to be continuous in (0 ,0)? I tried this:

piecewise[{((x^4*y^2)/(x^8+y^4))*senx, (x,y)!=(0,0)}, {(L)}=(0,0)]

Semtítulo.png

But it doesn’t work. Thanks.

2

Hi Christopher,

There are several syntax errors in the code. Should be

Piecewise[{{(x^4*y^2)/(x^8 + y^4)*Sin[x], x != 0 && y != 0}, {L, x == 0 && y == 0}}]

This seems like a homework problem, so a hint. For the function to be continuous, L must have the same value as the first part of the piecewise at {0, 0}.

3

Thank you! And sorry for my English, not my primary language, that’s why “sin” is written “sen”.