Proof: sqrt(x) is Continuous using Epsilon Delta Definition | Real Analysis Exercises

We prove that f(x)=sqrt(x), the square root function, is continuous on its entire domain where it is real, from 0 to infinity including 0. 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 D that is within delta of c has an image within epsilon of c's image. However, our approach will actually force c into the denominator in our proof, so we will need to take care of continuity at 0 separately. Let me know if there are more epsilon delta continuity proofs you want to see! #RealAnalysis Epsilon Delta Definition of Continuity: https://youtu.be/O98eOlHyWmQ Proof f(x)=x is Continuous: https://youtu.be/8KS8giQ_35s Proof ax+b is Continuous using Epsilon-Delta Definition: https://youtu.be/1jrcXqV34gg Proof f(x)=|x| is Continuous: https://youtu.be/HTN2rldZCHc Proof f(x)=e^x is Continuous: https://youtu.be/CPWO8RsIBy8 Proof f(x)=sin(x) is Continuous: https://youtu.be/o_OsB2KF4mQ Real Analysis playlist: https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli #RealAnalysis #Math ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/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: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu My Music Channel: https://www.youtube.com/channel/UCOvWZ_dg_ztMt3C7Qx3NKOQ