Limits of Multivariable Functions - Calculus 3

This Calculus 3 video tutorial explains how to evaluate limits of multivariable functions. It also explains how to determine if the limit does not exist.

Angle Between Two Planes:

Distance Between Point and Plane:

Chain Rule - Partial Derivatives:

Implicit Partial Differentiation:

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Directional Derivatives:

Limits of Multivariable Functions:

Double Integrals:

Local Extrema & Critical Points:

Absolute Extrema - Max & Min:

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Lagrange Multipliers:

Triple Integrals:

2nd Order - Differential Equations:

Undetermined Coefficients:

Variation of Parameters:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[johnch]

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[janeh]

0:00 direct substitution
0:43 manipulating equation to allow direct substitution
1:53 proving the limit D.N.E.
4:15 proving the limit D.N.E.
6:59 direct substitution
7:35 proving the limit D.N.E.
12:40 manipulating equation to allow direct substitution
15:20 using parametric curves

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[uke]

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[samiabdullah]

16:43 last example the y -axis when z=0 and x=0 its equal 1over2 which not zero

[radityafajri]

I think in the last example, when we approach the function from the y-axis (which gives us x = 0 and y = 0), the result doesn't equal to zero. So, from that, we can conclude that the limit DNE.

[jeenagurungfuenjnsvuc]

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[vinniesanchez]

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[quamos]

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[georgesadler]

Professor Organic Chemistry Tutor, thank you for solving Limits of Multivariable Functions in Calculus Three/ Multivariable Calculus. In some cases, Polar Coordinates can also be used to evaluate Limits of Multivariable Functions in Multivariable Calculus. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

[nikhilavishek]

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[mentor__adriansyahariak]

16:36, I'm sorry but if I check with lim y->0 which is (x=z=0), i got 1/2, isn't it?

[ycvllim]

question about the last problem, is it okay to let x, z=0 and the value becomes y^2/2y^2 which keeps value 1/2 and can say it's limit dne?

[Max-cubw]

Just a question, for the last problem, approaching from the y-axis, leaving x=0 and z=0 wouldn't you get 1/2 which also proves the limit DNE?

[bjornvanderlande]

really good video thanks, just had a question. In the last example you stated that this problem couldnt be solved by travelling over a certain axis, but if we travel over the y axis this limit becomes y^2/2y^2 which is 1/2 which is different than going over the x or z axis so the limit doesnt exist. Or am I overlooking something?