Let a be a nonzero constant such that a + 55. Letax? + sin? y5522 + y?Which of the following statements is correct?f(x, y) =and let L = lim(z,) »(0,0) f(x, y).O L=1O L does not exist because f is undefined at (0,0). (ffonksiyonu (0,0) noktasında tanımsız olduğu için Lyoktur).O L=a/55O Lexists if a=56 because in this case the limit as (x,y) goesto (0,0) along x=0 is the same as the one along y=x.(Eğer a=56 ise limit vardır çünkü bu durumda x=0 ve y=xdoğruları üzerinde limitler aynıdır.)O L does not exist because the limit as (xy) 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 olduğuiçin L yoktur.)

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Let a be a nonzero constant such that a + 55. Let ax? + sin? y 55x² + y² f(x, y) = and let L = lim(z,p) >(0,0) f(æ, y). Which of the following statements is correct?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Concept explainers

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:

Question

Let a be a nonzero constant such that a + 55. Let
ax? + sin? y
5522 + y?
Which of the following statements is correct?
f(x, y) =
and let L = lim(z,) »(0,0) f(x, y).
O L=1
O L does not exist because f is undefined at (0,0). (f
fonksiyonu (0,0) noktasında tanımsız olduğu için L
yoktur).
O L=a/55
O Lexists if a=56 because in this case the limit as (x,y) goes
to (0,0) along x=0 is the same as the one along y=x.
(Eğer a=56 ise limit vardır çünkü bu durumda x=0 ve y=x
doğruları üzerinde limitler aynıdır.)
O L does not exist because the limit as (xy) 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.)

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