► My Limits & Continuity course: https://www.kristakingmath.com/limits-and-continuity-course
The conjugate of any binomial term a+b is just the same binomial, but with the sign flipped in the middle. So if the original binomial is a+b, then its conjugate is a-b. If the original binomial is a-b, then its conjugate is a+b.
It makes sense then that the conjugate method for solving limits involves multiplying both the numerator and denominator of a rational function by the conjugate of either its numerator or denominator.
If we're going to use this method, then we have to identify either the numerator or denominator of the original fraction as a binomial term. Then we'll find the conjugate of this binomial and, to avoid changing the value of the original function, make sure to multiply both the numerator and denominator by the same conjugate, so that in effect we're multiplying by 1.
This method is usually use when the binomial term includes a square root, because multiplying by the conjugate will cancel the square root and make it easier for us to solve for the limit.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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Tagged under: limits continuity,conjugate,Krista King,canceling,conjugate method,solving limits,limits, ,expert,square roots,calculus,educational
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