Proof: ax+b is Continuous using Epsilon Delta Definition

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We prove that f(x)=mx+b, a general linear function, is continuous on its entire domain - 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 D that is within delta of c has an image within epsilon of c's image. In this case, it will be very easy, with one sidenote necessary for the m=0 case of a constant function. Let me know if there are more epsilon delta continuity proofs you want to see!

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Solid math.

A frustration I always had, when first learning epsilon-delta, was that the super easy examples always seemed like exercises in circular logic. In this particular case, my mind goes to, "okay, so all we've shown is that the slope of a line is the slope of a line". I realize that's not the lesson, but that's what it feels like.

More instructive to me was something like y = x^3, or y = 1/(x^2 + 1).

kingbeauregard
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Can you teach inscribe angle and all the term related to circle 🥲
Huge fan from india

ulgbtty