by-considering-different-paths-of-approach-show-that-the-functions-in-exercises-35-42-have-no-limi-5

Question

By considering different paths of approach, show that the functions in Exercises $35-42$ have no limit as $(x, y) \rightarrow(0,0) .$
$$
g(x, y)=\frac{x-y}{x+y}
$$

Uma Kumari · Accepted Answer

in this problem by considering different parts off. Coach needs to be shown that the function that has given G X Y is equals two X minus Y or X plus y has no limits as X Y approaches +00 are considering different parts off approach along XX is where why will be zero. They get limit. X Y approaches 00 x minus Y or X plus y is equals toe limit x zero approaches 00 X minus zero over X plus zero we get limit eggs zero approaches 00 x or x We get limit exceed Oh, approaches 00 one that before we get one now considering part off approach alone, Why exist where X will be zero limit Ex lie approaches 00 x minus Y or x plus y We get limit zero by approaches 00 zero minus y over zero plus y. Now, by solving this, we get limit. Zero vie approaches 00 minus y or by we get minus one. Now, as the parts why is equals to zero and X is equal to give zero give different values for the limit. Hence the function. G X y is supposed to X minus Y or X plus y has no limits as X Y approaches 00 that&#x27;s a solution.

Uma Kumari · Answer

in this problem, we are given G X y is equals toe X plus y over X minus y. Now it needs to be shown that the function as no limits as X Y approaches 00 We cannot find the limit by direct substitution over examine alone. Why is it was toe K X. Therefore it becomes limit. X y approaches 00 along. Why is it once took a eggs? The K is not equal toe minus five x plus Why or X minus y, so this will become limit. X approaches zero X plus k x or X minus K x on we get Lim X approaches. Zero eggs, one plus K or ex, followed by one minus k. We get limit X approaches zero one plus K or one minus game. We get one plus K or one minus k. Therefore, the given function has different limit or different values off gay at he Nordic will tow minus one. So that&#x27;s the solution

Uma Kumari · Answer

in this problem, consider the fallen function. F X Y is equals two X y or model X Y off. The objective is to show that about function has with no limit as X Y approaches 00 By considering different parts of approach, the limit cannot be found by direct substitution. Because this is 0/0 along the girl. Why is it was okay. X X is not equal to zero before the limit becomes X Y approaches 00 alone. Why is equals K X and he is not ableto zero x y Oh, a model ex wife is it was toe limit Eggs approaches zero ex military icky eggs. Oh, uh, model X multiply GX, which will give limit X approaches zero k x square model K X square, which will give us limit X approaches zero j x square over model. Okay, Malita X square and finally gives us Lim X approaches. Zero Okay, over more. Okay, So if the value off K is greater than zero, then the limit will be one. And if that day is less than zero, then the limit will be minus one. That is, the limits are different than the approach is different. Therefore, the function f x y is equals toe X Y or Model X Y has no limits as X Y approaches 00 so that&#x27;s a solution.

Uma Kumari · Answer

it is given that OPEC&#x27;s comma y is equal to X squared plus y divided by life, the limit cannot be found their direct substitution. So we will examine age alone. Y Z equals toa que x Square, then the limit. X com abidance to zero comma zero along provide is equals Tok X choir, where okay is not equal to zero. A queer plus y divided my wife. It would become Limit extends to zero X squared plus cake square divided by K X Square. It would be equals to limit extends to zero X square into one plus k. Be worried Becky X, where which is equals. Toe limit extends to zero one plus K divided by King, which is equals toe one plus K divided by King. That&#x27;s the function H has different limit for different values. Kaskey on is not equals to zero

Uma Kumari · Answer

consider the following function h of X comma by is equals toe Take square by a Paul X to the power four plus by square. The objective is to show that the above function has no limits as X comma vitamins to zero comma zero by considering different part off approach. The limit cannot be found by direct substitution method because by direct substitution, which gives the 00 indeterminate for now, examine the value of F along parabolic alot that ain&#x27;t at zero comma. Zero along the curve eyes equals two key X were coma access not equals to zero. The above function becomes h of X comma by this equals toe X square into why divided by X to the power of whole plus Vice square, which is equals two X where in two cakes where have divided blood x to the power full plus k x squared whole square By simply find it, we get que upon one plus k square, then lim X comma vitamins to zero comma zero along buys equals to play it square. It affects comma by is equal to lim X comma vitamins to zero comma zero along bicycles to take square que upon one plus case where it is equals toe que upon one plus K square. The limit varies with the part off approach. If X comma via tends to zero comma zero along the parable Love I is equal to X square that is que is equals to one. Then the limit is when upon one plus one square is equals to one upon to If x comma violence to zero comma zero along the X axis, that is why is equals to zero. It means that case also equals to zero than the limit has zero upon one plus zero, which is equals to zero by the two path test. If has no limit as it&#x27;s common guidance to zero comma zero does the given function has no limit as X comma vitamins to zero comma zero

Uma Kumari · Answer

in this problem, consider the function F X y physicals, toe extra, about four minus y square or actually the power four plus twice where. How the objective is to show that the function has no limit by considering different parts of approach on the limit cannot be found by direct substitution, which gives the indeterminant form that will be 0/0. Now examine the limit off the function along the different parts. That is why is equals to K X square so that so take the limit as limit X Y approaches 00 alone. Why is equals toe K X Square, which gives us f x y Z equals toe limit. X y approaches 00 along. Why is it was to be expire X to the power four minus vice square over. It&#x27;s about four. Bless my square now, putting the values or pie, we will get limit X approaches zero X to the power four minus K X square, Whole square over. Excited about four plus a X Square whole square now, But simply find this. We will get limit. X approaches zero X to the path forward one minus games. Where over extra about four bunless is where we will get one minus case where over one plus is where therefore the value off the limit depends on the value off constant K. Hence the value off limit is wearing with the value off. Hey, now for K is equals to one the value X fight approaches 00 along the parabola. Why is it was two x square and the limit is limit. X y approaches 00 along Why is equals two x square f x y is It was toe one minus one whole square over one plus one whole square because her key is it was 21 By solving this really get zero over to that is it was 20 Hence for K is equals to one that along the parabola why is equal to X square and the limit is zero. Now we&#x27;ll ask poor he is equals to zero the value exp I approaches 00 along the x X is Why is it was 20 and the limit will be limit. X y approaches 00 along why is equals to zero f x y is equals toe one minor, zero whole square over one plus zero whole square. Because here K is equals to zero by solving the civilian one or one is equals to one hand, or K is equals to zero. Along the X axis is why is equals to zero and the limit is one. Therefore, the function F x y have different limits or different values. Uh, yeah, hands the limit off function. F X Y does not exist, so that&#x27;s the solution.

Problem

By considering different paths of approach, show …

Problem 39 Medium Difficulty

By considering different paths of approach, show that the functions in Exercises $35-42$ have no limit as $(x, y) \rightarrow(0,0) .$
$$
g(x, y)=\frac{x-y}{x+y}
$$

Answer

As paths, $y=0$ and $x=0$ , give different values for the limit, hence the function
$g(x, y)=\frac{x-y}{x+y}$ has no limit as $(x, y) \rightarrow(0,0)$

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As paths, $y=0$ and $x=0$ , give different values for the limit, hence the function$g(x, y)=\frac{x-y}{x+y}$ has no limit as $(x, y) \rightarrow(0,0)$

Thomas Calculus

Lily A.

Heather Z.

Kayleah T.

Michael J.

Vectors Intro

Vector Basics - Example 1

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. GiordanoThomas Calculus

Lily A.

Heather Z.

Kayleah T.

Michael J.

As paths, $y=0$ and $x=0$ , give different values for the limit, hence the function
$g(x, y)=\frac{x-y}{x+y}$ has no limit as $(x, y) \rightarrow(0,0)$

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano

Thomas Calculus