Why is the limit 2025? a simple plug and chug limit gone wrong

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Homework Help Overview

The discussion revolves around evaluating a limit in a multivariable context, specifically as (x,y) approaches (5,-2) for the expression (x^5 + 4x^3y - 5xy^2). Participants are exploring the implications of substituting values directly into the expression and questioning the existence of the limit.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the validity of direct substitution into the limit expression, with one participant questioning the existence of the limit based on their calculations. Others suggest that direct substitution yields a different result, prompting a reevaluation of the initial approach.

Discussion Status

The conversation is ongoing, with some participants providing clarifications on the method of evaluating limits. There is recognition of potential errors in calculations and a suggestion to reconsider the approach taken by the original poster.

Contextual Notes

One participant notes a misunderstanding in the application of limit concepts, comparing it to a simpler limit scenario, which highlights the need for careful consideration of the approach to multivariable limits.

mr_coffee
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Hello everyone i have the following prlbem:
lim (x,y)->(5,-2) (x^5+4x^3y-5xy^2);

So i let y be fixed at 0 and let x equal 5, and i got 5^5 which is 3125, if i let 0, and y be -2 i get 0. Doesn't this mean the limit doesn't exist? but it says its 2025, ?
 
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Just plug in 5 for each x value and -2 for each y value, you get 2025. You were doing something completely different.
 
ohhh i did that before and i messed up on multipcation thank u
 
What you're doing in your first post is like saying that if you have:

[tex]\lim _{x \to 7} x^2[/tex]

and you plug in x = 3 to get 9 and plug in x = 10 to get 100, then the limit doesn't exist.
 

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