How To Evaluate Limits of Radical Functions | Calculus

This Calculus video tutorial explains how to evaluate limits with radical functions such as square root functions.

How To Evaluate Limits From a Graph:

Evaluating Limits By Factoring:

Limits of Rational Functions :

Limits of Radical Functions:

Limits of Trigonometric Functions:

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How To Find The Limit at Infinity:

Infinite Limits + Vertical Asymptotes:

Limits at Infinity With Radicals:

Limits of Absolute Value Functions:

Limits of Composite Functions:

The Squeeze Theorem:

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Limits and Logarithms:

Limits of Exponential Functions:

Piecewise Functions - Limits:

3 Step Continuity Test:

Continuity and Differentiability:

Limits - Test Review:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[uvaldoandIsaaclopez]

Dude you are by far the most excellent teacher and I’m blown away by the vastness of your knowledge! Thanks man!!!

[gregoryg.philips]

Thank you so much. I was having a little difficulty with my math 203 assignment but your explanation has given me a clearer understanding of the problem. May God bless you. 🙏

[ashtonmeyer]

Question: How do you know when to take the conjugate of the numerator or the denominator?

[kevingarita]

Great teacher! thanks a lot brother, I spent like 2 hours trying to find examples like these.

[georgesadler]

MR. Organic Chemistry Tutor, thank you for Evaluating Limits of Radical Functions using algebra tricks and tools. Limits problems in Calculus uses a heavy dose of algebra.

[KingGregforever]

Thanks a lot 🙏 but is it necessarily compulsory to multiply top and bottom with the conjugate with the denominator?

[alphasaffi]

My mentor thank you very much may God 🙏 bless you sir.

[phathiscreations]

So grateful for you. Thank you so much. That was of great help...🌸

[ladymichellebarlisan]

this example is quiet hard:( . In some parts, the fraction was multiplied with the numerator and other parts were multiplied with the denominator

[Ivan-qvxh]

are you able to explain how to show the limit of 1/x as x approaches 0 does not exist using the e-d definition? I feel like it would be pretty good to look at since the function seems so simple yet so difficult to prove DNE, i've been stuck on it for so long.

[hluu]

Can you also have used l'hopital's rule?

[freeguylota]

Are we meant to multiply by the numerators conjugate or the denominators own?

[efloof]

Calculus got me watching ts on my breaks

[CaptainEchoPH]

In the first example, can you instead use the numerator as a conjugate or should it always be the conjugate of the denominator when there are radicals in a fraction?

[unkownlast]

Why did (√7-x)(+2) equalled to +2√7-x ?

[Cloud]

What sorcery is this? Lol I was confused by a similar question involving the replacement rule, limits, and square roots. Thanks.

[RaffaelloLorenzusSayde]

Is multiplying by conjugate strictly for square roots?

[deathmonk]

I'm watching this because im bored

[malakayman]

Your the best my teacher is way too fast

[jan-willemreens]

... An alternative way of solving this limit as follows: lim(x-->3)((sqrt(12 - x) - 3)/(sqrt(7 - x) - 2)), Multiply the limit by ((7 - x) - 4)/((12 - x) - 9) (= 1/1) and split the limit in two limits according to the multiplication limit law: lim(AB) =lim(A)lim(B) as follows: [ lim(x-->3)((sqrt(12 - x) - 3)/((12 - x) - 9)) ][ lim(x-->3)((7 - x) - 4)/(sqrt(7 - x) - 2)) ], Treat (12 - x) - 9 and (7 - x) - 4 as differences of two squares: (12 - x) - 9 = (sqrt(12 - x) - 3)(sqrt(12 - x) + 3) and (7 - x) - 4 = (sqrt(7 - x) - 2)(sqrt(7 - x) + 2), After cancelling the common factors (sqrt(12 - x) - 3) and (sqrt(7 - x) - 2) of respectively limit #1 and #2 we obtain the final solvable limit form of: [ lim(x-->3)(1/(sqrt(12 - x) + 3)) ][ lim(x-->3)(sqrt(7 - x) + 2) ] = [ 1/(3 + 3) ][ 2 + 2 ] = (1/6)(4) = 4/6 = 2/3 ... Hoping this way is also appreciated a bit (less algebra)... Thank you for all your valuable math efforts, Jan-W