If you intentionally set up a function to have different limits along different lines, I dont (sic) see what else you can do with Mathematica. Do each of the following in Wolfram Alpha (a.) Find the limit sin (3x) lim x>0 (b.) Compute the first and second derivative f(x) e-x2 cos (3x).
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Software engine implementing the Wolfram Language. 2 begingroup I think if you write that as an answer on an exam, it will be marked wrong. Central infrastructure for Wolframs cloud products & services. 586 3 3 silver badges 14 14 bronze badges endgroup 2. For that you have to show the independence of the result on the direction of the line. 1,449 2 2 gold badges 8 8 silver badges 19 19 bronze badges. With Limit, you're always restricted to a line in the larger space, and you can't make statements about the existence of the limit in the sense of the higher-dimensional space. this thread on Mathematica.SE which goes at length into explaining one can possibly try and do it - spoiler, it's complicated. (actually, I'd go further and suggest: Do not try limits in more than one real variable with Mathematica or WolframAlpha.) The key message is:ĭo not try limits in more than one variable with Mathematica or WolframAlpha.
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Sometimes there may be many solutions corresponding to many curves where the denominator is zero the code above would have to be adapted to handle such cases.This is only to complement the excellent answer of StackTD, who correctly shows that you are right - the limit does not exist (as one can find two different paths to the origin along which the limits of the function differ).
Numerical approximationĪ nonrigorous way to go is to get numerical evidence. WolframAlpha Notebook Edition combines the best of both WolframAlpha and Mathematica into a single, unified tool perfect for teaching and learning.
A third method of testing for nonexistence is included at the end. Course Assistant Apps » An app for every course right in the palm of your hand. MathWorld » The webs most extensive mathematics resource. WolframAlpha » Explore anything with the first computational knowledge engine. The first two methods below apply this concept. Mathematica » The 1 tool for creating Demonstrations and anything technical. WolframAlpha calls Mathematicas built-in function Limit to perform the computation, which doesnt necessarily perform the computation the same as a human would. It fails here because Maximum and Minimum fail on f.
If you have WolframAlpha Pro, you can do computations with a higher limit on computational time but I often find that the computation times out even so. The idea behind the function lim in this answer was to use Maximum and Minimum to find bounds on the function and apply the squeeze theorem. If a limit exists that is independent of path when restricting to real variables, then, on an especially good day, WolframAlpha might tell you what that limiting value might be. WolframAlpha imposes a limit on the amount of computational time it allows for each computation.
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This free online calculator will help you to.
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As pointed out in the answers to this question, finding multivariable limits automatically computationally is full of pitfalls. This calculator for solving limit use the widget from Wolfram Alpha LLC. With the commonly used 95 confidence limit, 0.05 (since 10095 is 5.
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