Limit of x*sin(1/x) as x approaches Infinity | Calculus 1 Exercises

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We show the limit of xsin(1/x) as x goes to infinity is equal to 1. This means x*sin(1/x) has a horizontal asymptote of y=1. We'll also mention the limit with x at negative infinity, which is found in the same way and is also equal to 1. To figure this all out, we'll give 1/x a different name, and see that we actually have a limit in the form sin(x)/x with x approaching 0, which is a fundamental trigonometric limit equal to 1! #Calculus1

What other horizontal asymptotes/limits at ∞ would you like to see?

Proof for Limit of sin(x)/x: (coming soon):

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WrathofMath

Quick and straight to the point, great way to solve this limit. Thank you.

CeCealYT

I really apreciate that you pronounce very clear every single word that you said. My native language is spanish. So, sometimes it is difficult to me to understand when people explain maths in english. Thank you! u are awesome!!

kat_bluesky_

I am from india, but this lecture very helpful for me

TanuchMahananda-kvmh

Very clever substitution! Definitely worth remembering! Thanks for this video. 👍

punditgi

I never comment on these type of videos, but this truly wrapped my head around this limit topic thank you

kapsxd

Lim x tend to infinity xsin(1/x)
Can be written as sin(1/x)whole divided by(1/x)
So 1 we can also do like this ?

studymotivation

Great explanation! I appreciate how clear you were. Thank you!

tecknitian

Thank you very much for this nice and detailed explanation 🌹🌹

alyaaal_amili

Hey i have doubt
Of i use sandwich therom
-1<=sin (1/x)<=1
Now multiply with x on both sides
-x<=xsin(1/x)<=x and now if i do lim x tends to infinity on boths sides
Negative infinity<=lim x tends to infinity sin(1/x)<=positive infinity
Which is violating the rule of sandwich theorm which means limit does not
Plzzzz reply

m.saiujwalchinnu

using abslon and delta to prove limt X×sin(1/X)=1, if X goes to infinity, can you solve it, please

hananfneer

Can you explain a bit about how do we know if it approaching positive infinity from just looking at the problem, still a beginner at limit, can anyone please explain it?

svnspell

You don't understand how bad I wish you replaced my math professor

lukedepireux

Sir I need th prov of the limit (sin x)/x equal 1

djabermherzi

ذا السؤال كان غلطي الوحيد بالأختبار وبعد الاختبار مخي كان بينفجر
كيف الجواب١!!!
بس وضحت الحين😅

why

Sin 1/x that is sin 1/infinity we know that 1/infinity is O sin0 is 0 so why is the answer not zero pls answer someone

Kiran-vwib

You didn’t generalize the special limit by writing it that way and it made it really confusing. Just use x and say it’s role is of a dummy variable

coreymonsta

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