Quarto Markdown (.qmd) Testing

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January 1, 2025

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Theorem 1 (Quadratic Formula) x=b±b24ac2a

Proof. by (a+b)2=a2+2ab+b2 ax2+bx+c=0 (a0)x2+bax+ca=0(x+b2a)2=ca+b24a2(x+b2a)2=4ac+b24a2x+b2a=±b24ac4a2x=±b24ac4a2b2ax=±b24ac2ab2ax=b±b24ac2a

Definition 1 (Metric Space) A metric space is a set Mwith a function d:M×MR such that:

  1. d(x,y)0(Non-negativity)
  2. d(x,y)=0 if and only if x=y
  3. d(x,y)=d(y,x) (Symmetry)
  4. d(x,z)d(x,y)+d(y,z) (Triangle inequality)

Definition 2 (The limit of a sequence) Suppose an is a convergent sequence, and LR is the limit

ϵ>0,NN,nN,|anL|<ϵ

Note: the order of the quantifier is , ,

asd

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H6

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What is JavaScript ?

console.log("Hello")

Fundamental Theorem of Calculus

abf(x)dx=f(b)f(a)

Thm: Multiple Lines Theorem

(1)ax2+bx+c=0x=b±b24ac2a

Tip 1

This is a callout

Theorem 2 This is a theorem example for testing reference


Quote:

Nested Quote:

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Google

https://quarto.org/docs/get-started/

Figure 1: alt text

A\B B1 B2
A1 A1 x B1 A1 x B2
A2 A2 x B1 A2 x B2

Footnotes

  1. You can embed pdf into your document↩︎

  2. You can use @ to refer to the sources↩︎