How to rationalize the radical to evaluate a limit

👉 Learn how to evaluate the limit of a function by rationalizing the radical. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time.
The limit of a function is usually evaluated by direct substitution of the value which the variable tends to. When the function is a rational expression such that direct substitution leads to zero in the denominator, we find a way to either eliminate the denominator by multiplying both the numerator and the denominator by a common factor (this can involve rationalization) or decompose the denominator and the numerator into constituent parts so that like terms can cancel out.

Organized Videos:
✅The Limit
✅Evaluate Limits of Complex Fractions
✅Evaluate Limits of Polynomials
✅Evaluate Limits of Rational Expressions
✅Evaluate Limits with Square Roots
✅Evaluate Limits with Trig
✅Limits of Piecewise Functions
✅Evaluate Limits with Transcendentals
✅Evaluate Limits Difference Quotient
✅Evaluate Limits from a Graph
✅Evaluate Limits of Absolute Value
✅Evaluate Limits of Square Root
✅Holes and Asymptotes of Rational Functions
✅Learn about Limits
✅Find the Value that makes the Function Continuous
✅Is the Functions Continuous or Not?
✅Evaluate Limits using a Table of Values
✅Evaluate Limits at Infinity

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[ILoveCalculus]

you're going to be the reason why I get my comp-sci degree. Thank you sir

[yonathanwondimu]

When you have the same problem for homework 😏

[jan-willemreens]

...A slick and succinct way of solving the same indeterminate (0/0) limit is as follows: lim(x-->3)((sqrt(x + 1) - 2)/(x - 3)) (rewrite the denominator x - 3 as: x - 3 = (x + 1) - 4 and treat this expression as a difference of two squares: (x + 1) - 4 = (sqrt(x + 1) - 2)(sqrt(x + 1) + 2) and finally cancel the common factor (sqrt(x + 1) - 2) of numerator and denominator, resulting in the solvable limit: lim(x-->3)(1/(sqrt(x + 1) + 2)) = 1/(2 + 2) = 1/4... I hope this method by factoring is also appreciated, at least it is clear and short! Jan-W

[DheshViloria]

Sir can you explain why you need to rationalized the equation instead of using conjugate?

[WomBat_t]

your lessons helps with my basic calculus

[otherlego]

Why aren’t we using distributive property?

[julaicaresus]

Thank you a lot sir you save my life<3

[zee]

im pretty sure you add -2+2=0 so it should just be x in numerator

[ReviewMMA]

Um how did he get rid of the -4? Literally just disappeared he didnt explain it

[ninjaofcake]

Even now, this man is saving lives. His way of teaching is understandable and straightforward. Kudos! 🫡