Find the limist if it exists for a 3-variable function

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SUMMARY

The discussion focuses on finding the limit of the function lim(e^(-x*y) * sin(π * z/2)) as (x,y,z) approaches (3,0,1). The key method for determining the existence of the limit involves substituting the values of x, y, and z into the function and assessing continuity at that point. The participants emphasize the importance of substitution and continuity in evaluating limits for multi-variable functions.

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  • Familiarity with continuity concepts in mathematical functions.
  • Knowledge of trigonometric functions, particularly sine and its properties.
  • Experience with exponential functions and their behavior in limits.
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  • Study the concept of limits in multi-variable calculus, focusing on three-variable functions.
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  • Explore examples of limits involving exponential and trigonometric functions.
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Students studying calculus, particularly those tackling multi-variable limits, as well as educators seeking to clarify the concepts of continuity and limit evaluation in three-variable functions.

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Homework Statement


lim(e^(-x*y) * sin( pi * z/2) as (x,y,z) approaches (3,0,1)

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The Attempt at a Solution


i know how to find the limit exists or not for a 2-variable function which is just set x=o;y=0;x=y
how can this method applies here
 
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Remember that the first approach when computing any limit is to just substitute the point that you are approaching.
 
n!kofeyn said:
Remember that the first approach when computing any limit is to just substitute the point that you are approaching.

And think about whether the function is continuous there, right?
 

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