My ultimate introduction to the epsilon-delta definition of limits in calculus! The epsilon-delta definition of a limit is commonly considered the hardest topic in Calculus 1 (it's also the important part at the beginning of real analysis). The best way to understand this precise definition of a limit is to actually use an actual value for epsilon first, then solve for the corresponding delta. When writing epsilon-delta proofs for limits, be sure to set it up: given, choose, suppose, and check!

εN definition (finite limit at infinity): 👉    • epsilon-N definition for a limit at i...  

Check out more examples of proving limits with the εδ definition:
linear, square root, and quadratic 👉    • limits with epsilon-delta definition!...  
1/x and x^3 👉    • limits with epsilon-delta definition!...  
"a taste of real analysis" 👉    • Proving x^2 is continuous but NOT uni...  

0:00 the εδ definition of a limit is the hardest topic in calculus 1
1:34 limit of sqrt(2x+1) as x approaches 4
4:14 if epsilon is 0.2, how to find the biggest delta
10:27 writing the εδ proof

Get an epsilon-delta hoodie: 👉 https://blackpenredpen.creator-spring... Use "WELCOME10" for 10% off
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