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Apostila - Minicurso de HP Prime

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MINICURSO DE HP PRIME 
MINICURSO DE HP PRIME 
 
─
https://petequfpr.wixsite.com/peteq
https://petequfpr.wixsite.com/peteq
https://epequfpr.wixsite.com/epeq
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
𝑦 − 𝑦0
𝑥 − 𝑥0
= 
𝑦1 − 𝑦0
𝑥1 − 𝑥0
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
⁰
𝑌−88
32−20
100−88
40−20
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
→ →
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 → →
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
https://www.hpcalc.org/details/7747
 
 
 
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
Σ
Σ 
ẋ 
 
σ
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
Σ
Σ
ẋ
Σ
Σ
σ
ẏ
Σ
Σ
σ
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
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file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeqfile:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
ξ ξ ξ ξ
ξ
ξ ξ
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
⇌ ⇌
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
𝑥 + 2 = 0
𝑥2 + 𝑥 − 2 = 0
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
𝑥2 + 𝑥 − 2 =
𝑥 + 3
𝑥 + 4
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
𝑥2 + 𝑥 − 2 = 0
𝑥2 + 𝑥 − 2 =
𝑥 + 3
𝑥 + 4
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
𝑥2 + 𝑥 − 2 =
𝑥 + 3
𝑥 + 4
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
𝑥 + 2 = 0
𝑦 = 2 ∗ 𝑥 + 𝑤
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
𝑃 =
𝑅𝑇
𝑉−𝑏
−
𝑎
𝑉2
𝑎 =
27(𝑅. 𝑇𝐶)
2
64𝑃𝐶
𝑏 =
𝑅. 𝑇𝐶
8𝑃𝐶
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
ε ρ
1
√𝑓
= −2,0 log (
𝜀
𝐷⁄
3,7
+
2,51
𝑅𝑒√𝑓
)
𝑣 =
𝑄
𝐴
=
4. 𝑄
𝜋𝐷2
=
4.0,0111
𝜋. 0,10162
= 1,37 𝑚/𝑠
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
𝑅𝑒 = 
ρ. v. D
µ
=
998,204.1,37.0,1016
1,0016.10−3
= 138720,059 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
{
2𝑥 + 𝑦 − 2𝑧 = 10
3𝑥 + 2𝑦 + 2𝑧 = 1
5𝑥 + 4𝑦 + 3𝑧 = 4
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
{
𝑥 + 𝑦 + 𝑧 = 4
2𝑥 + 5𝑦 − 2𝑧 = 3
𝑥 + 7𝑦 − 7𝑧 = 5
{
𝑥 + 𝑦 + 𝑧 = 6
𝑥 − 𝑦 + 𝑧 = 4
𝑥 + 𝑧 = 5
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
{
2𝑥 + 𝑦 − 2𝑧 = 10
3𝑥 + 2𝑦 + 2𝑧 = 1
5𝑥 + 4𝑦 + 3𝑧 = 4
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
{
𝑥 + 𝑦 + 𝑧 + 𝑡 = 0
𝑥 + 𝑦 + 𝑧 − 𝑡 = 4
𝑥 + 𝑦 − 𝑧 + 𝑡 = −4
𝑥 − 𝑦 + 𝑧 + 𝑡 = 2
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
{
𝑥2 − 𝑦2 = 2
𝑥2 −
𝑦2
9
= 1
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
{
𝑥2 + 𝑦2 = 4
𝑦 = 𝑥 + 1
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
{
𝑦 = cos 𝑥 + 2
𝑦 = 1,5. ln (𝑥)
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
𝑦𝑖𝑃 = 𝑥𝑖𝑃𝑖
𝑠𝑎𝑡𝛾𝑖
γ
𝛾1 =
𝑦1𝑃
𝑥1𝑃1
𝑠𝑎𝑡
𝛾1 =
𝑃
𝑃1
𝑠𝑎𝑡 =
319
306
= 1,04248
𝛾2 =
𝑃
𝑃2
𝑠𝑎𝑡 = 1,13929
ln 𝛾1 =
𝐴′
(1 +
𝐴′𝑥1
𝐵′𝑥2
)
2
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
ln 𝛾2 =
𝐵′
(1 +
𝐵′𝑥2
𝐴′𝑥1
)
2
ln 1,04248 =
𝐴′
(1 +
𝐴′0,65
𝐵′0,35
)
2
ln 1,13929 =
𝐵
(1 +
𝐵′0,35
𝐴′0,65
)
2
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
▶
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
 
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteqfile:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
lim
𝑥→0
(
2𝑥 − 1
𝑥
)
lim
𝑥→0
(cos
1
𝑥
 )
file:///C:/Users/lucas/Downloads/petequfpr.wixsite.com/peteq
file:///C:/Users/lucas/Downloads/epequfpr.wixsite.com/epeq
─
https://petequfpr.wixsite.com/peteq
https://petequfpr.wixsite.com/peteq
https://epequfpr.wixsite.com/epeq

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