Скачать или смотреть Proof: f(x) = |x| is Continuous using Epsilon Delta Definition | Real Analysis Exercises

We prove that f(x)=|x|, also known as f(x)=abs(x), the absolute value function, is continuous on the real numbers. We complete this proof using the epsilon delta definition of continuity of a function at a point. To do this, we simply take an epsilon greater than 0 and an arbitrary point c from our domain, then go through the motions of finding a delta greater than 0 so that any x in R that is within delta of c has an image within epsilon of c's image. We'll need the reverse triangle inequality theorem and not much else! Let me know if there are more epsilon delta continuity proofs you want to see!

Proof: Reverse Triangle Inequality Theorem:    • Proof: Reverse Triangle Inequality Theorem...  
Epsilon Delta Definition of Continuity:    • This is the Epsilon Delta Definition of Co...  
Proof f(x)=|x| is Continuous:    • Proof: f(x) = |x| is Continuous using Epsi...  
Proof f(x)=sqrt(x) is Continuous:    • Proof: sqrt(x) is Continuous using Epsilon...  
Proof f(x)=e^x is Continuous:    • Proof: e^x is Continuous using Epsilon Del...  
Proof f(x)=sin(x) is Continuous:    • Proof f(x)=sin(x) is Continuous using Epsi...  

Real Analysis playlist:    • Real Analysis  

#Math #RealAnalysis

★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons  
◆ Donate on PayPal: https://www.paypal.me/wrathofmath

Thanks to Robert Rennie, Barbara Sharrock, and Rolf Waefler for their generous support on Patreon!

Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/

Follow Wrath of Math on...
● Instagram:   / wrathofmathedu  
● Facebook:   / wrathofmath  
● Twitter:   / wrathofmathedu  

My Music Channel:    / @emery3050