How To Find The Limit At Infinity
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- Опубликовано: 2 окт 2024
- This calculus video tutorial explains how to find the limit at infinity. It covers polynomial functions and rational functions. The limit approaches zero if the function is heavy at the bottom or if the degree of the denominator exceeds that of the numerator. The limit approaches a constant value if the degree of the numerator and the denominator is the same. If the numerator has a higher degree, the limit will approach positive or negative infinity.
Full-Length Math & Science Videos:
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Introduction to Limits:
• Calculus 1 - Introduct...
How To Evaluate Limits From a Graph:
• How To Evaluate Limits...
Evaluating Limits By Factoring:
• Evaluating Limits By F...
Limits of Rational Functions :
• Limits of Rational Fun...
Limits of Radical Functions:
• How To Evaluate Limits...
Limits of Trigonometric Functions:
• Limits of Trigonometri...
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How To Find The Limit at Infinity:
• How To Find The Limit ...
Infinite Limits + Vertical Asymptotes:
• Infinite Limits and Ve...
Limits at Infinity With Radicals:
• Limits at Infinity Wit...
Limits of Absolute Value Functions:
• Limits and Absolute Value
Limits of Composite Functions:
• How To Find The Limit ...
The Squeeze Theorem:
• Squeeze Theorem
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Limits and Logarithms:
• Limits and Logarithms
Limits of Exponential Functions:
• Limits of Exponential ...
Piecewise Functions - Limits:
• Piecewise Functions - ...
3 Step Continuity Test:
• 3 Step Continuity Test...
Continuity and Differentiability:
• Continuity and Differe...
Limits - Test Review:
• One Sided Limits, Grap...
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Final Exams and Video Playlists:
www.video-tuto...
Limits - Free Formula Sheet:
bit.ly/3T3dD2X
Limits - Free Formula Sheet: bit.ly/3T3dD2X
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3:13, the expression can also be written as (x³(3-5x)), isn't that technically now insignificant,I don't get it,what are the requirements for insignificance? to be in + and - to each other or multiplication and divisions also consider it
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Way too much for solving these problems. Guys please study this.
It'll get you the same answer in a second.
- if highest degree is in the denominator, then the answer is always 0
- if highest degrees match on numerator and denominator, the answer is the leading coefficient of the numerator divided by the leading coefficient of the denominator
- if highest degree is on numerator, then the answer could either be infinity or negative infinity
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note 5:12 : Any time we have a bottom heavy function with the limit tends to infinity , its equal to zero
note 6:24 Any time you see same degree in numerator and denominator with limit tends to zero. Ans is coefficient of numerator/ coefficient of denominator
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in 10:33, why did you not multiply top and bottom by 1/(x^2) like before?
Yeah it is a bit odd that he did that... If you multiplied by 1/(x^2) instead you would still get the same answer, although the process would look a bit different. In general, when the highest degree in the numerator is greater than the highest degree in the denominator, the limit will not exist at a finite number and could be infinity or negative infinity. I explain this in one of my own calculus tutorials on this topic, which I will link here for you if you are interested. The part of my video that relates to your question can be found around 10 minutes and 40 seconds into it. Just use the video chapters to help you find it! Here is the link: ruclips.net/video/TgW5jKtFETY/видео.html Hope this helps! :)
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Find it difficult to even imagine the significance of this branch of limits, honestly... Like, why are we finding limits at infinity?
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Nice outro
Oh! This is where limit properties come in. This is the cervix.
Because Lim(a)(x/y) = Lim(a)(x)/Lim(a)(y)
So Limx->♾️ ((5x-7x³)/(2x²+14x³-9))
= Limx->♾️ 1/x³ (5x-7x³)/ Limx->♾️ 1/x³ (2x²+14x³-9)
= ... (5/x² - 7)/(2/x + 14 - 9/x³)
Limx->♾️ (5/x² - 7) is horizontal asymptote at y=0-7 = -7
Limx->♾️ (2/x + 14 - 9/x³) have one at y= 0+14=14
And using the Lim(a/b)= Lima/Limb rule, we get that the limit of the function as x approaches infinity= -7/14 = -1/2
today i didn't just learn limit at infinity, i also learned how much i hate fractions more
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expression (5+2x-x^3)/x >>>>> 5/x+2+x^2 result can be 5/x=0, 2 is real number and only x^2 is similar to first example.Thank sir for lessons
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Hello, i've got the question, why at 10:34 we multiply everything by 1/x, but not 1/x^2, if so, we'll get 6/0 = 0, before we were choosing the x with the highest power(x^2) and now not (just x) i'm confused now.
It must be divided by highest power of x in DENOMINATOR.
Besides, (number)/0 is not equal to 0, but math error
Number / 0 is actually taken as infinity
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If it’s infinity over infinity, what do we do then? @TheOrganicChemsitryTutor
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