Computing Multivariable Limits Algebraically

TYPO: The point (2,3) in the second example really should be (3,2) throughout. In our intro video on multivariable limits we saw how to show a limit does not exist by the two path test:https://www.youtube.com/watch?v=hxrnjxth8sA&list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd&index=12 In this video we're going to show that the limit of a multivariable function DOES exist by using a range of algebraic tricks such as factoring or multiplying by the radical conjugate. The idea is to manipulate the indeterminate form until such point as you can plug in the numbers. We also take a look at algebraic limit laws for multivariable functions. 0:00 Intro & 1st Example 1:50 Limit Laws 4:50 Factoring Example 7:17 Radical Conjugate Example **************************************************** COURSE PLAYLISTS: ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►DIFFERENTIAL EQUATIONS (Calc IV): https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 *************************************************** ► Want to learn math effectively? Check out my "Learning Math" Series: https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Want some cool math? Check out my "Cool Math" Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho **************************************************** ►Follow me on Twitter: http://twitter.com/treforbazett ***************************************************** This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria. BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett