xy Let f(r, y) : and let L lim(7,1) >(0,0) f(x, y). Which of the following statements is correct? 5x2 + 3y2 TY Türkçe: Eğer f(x, y) ve L = lim(z,p) »(0,0) f(x, y) ise aşağıdaki cümlelerden hangisi doğrudur? 5æ? + 3y? O L=3/8 O L does not exist because f(x,y) is not defined at (0,0). (f(x,y) fonksiyonu (0,0) noktasında tanımsız olduğu için L yoktur.) O L does not exist because the limit as (x,y) goes to (0,0) along the x-axis is different from the one along the line x=y. (x-ekseni ve x=y doğrusu üzerinde limitler farklı olduğu için limit yoktur.) O L does not exist because the limit as (x,y) goes to (0,0) along the x-axis is different from the one along the y-axis. (x-ekseni ve y-ekseni üzerinde limitler farklı olduğu için L yoktur.) O L=0 O L=1/8

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: