Why are epsilon delta proofs so hard?

Why are epsilon delta proofs so hard?

Personally, I find the epsilon-delta proofs start to get difficult when students have to prove that one part X is less than ϵ/2, another part Y is less than ϵ/2, so their sum X+Y<ϵ.

What is δ in calculus?

The two most common meanings are as the difference and the discriminant. The lowercase delta is used in calculus to mean the distance from the limit. The two meanings of the uppercase delta have formulas you can use to calculate them. The lowercase meaning is strictly a definition with no associated formula.

Who invented Epsilon Delta?

Bolzano
Although implicit in the development of calculus of the 17th and 18th centuries, the modern idea of the limit of a function goes back to Bolzano who, in 1817, introduced the basics of the epsilon-delta technique to define continuous functions.

Can Delta equal epsilon?

Therefore, since c must be equal to 4, then delta must be equal to epsilon divided by 5 (or any smaller positive value).

Can you move the limit to the inside of a square root?

Square root is a continuous function. Hence, we can bring in the limit inside the square root.

How do you use epsilon delta to prove a limit?

Using the Epsilon Delta Definition of a Limit

1. Consider the function f(x)=4x+1.
2. If this is true, then we should be able to pick any ϵ>0, say ϵ=0.01, and find some corresponsding δ>0 whereby whenever 0<|x−3|<δ, we can be assured that |f(x)−11|<0.01.

How do you prove a discontinuity of a piecewise function Epsilon Delta?

Prove discontinuity of piecewise linear function using epsilon-…

1. Let f(x)={2x+3 for x≥1,−x+5 for x<1.
2. f is continuous from the right at x≥1.
3. Let ϵ>0 be arbitrary.
4. Let x0≥1.
5. Let δ=ϵ/2.
6. Let x∈R and x0≤x
7. Thus |f(x)−f(x0)|=|2x+3−2×0−3|=|2x−2×0|=2|x−x0|<2δ=2ϵ/2=ϵ.

How do you write Epsilon Delta proofs?

To do the formal ϵ − δ proof, we will first take ϵ as given, and substitute into the |f(x) − L| < ϵ part of the definition. Then we will try to manipulate this expression into the form |x − a| < something. We will then let δ be this “something” and then using that δ, prove that the ϵ − δ condition holds.

Who is the real father of calculus?

Sir Isaac Newton
Sir Isaac Newton was a mathematician and scientist, and he was the first person who is credited with developing calculus.