SOLUZIONI NUMERICHE ESERCIZI
Transcript of SOLUZIONI NUMERICHE ESERCIZI
SOLUZIONINUMERICHEESERCIZI
Dott.ssa Elisabetta Bissaldi
Capitolo 0
Es. 0.1
1. ๐ = ๐. ๐๐ ๐/๐๐
Es. 0.2
1. ๐๐ญ = ๐ ร ๐๐๐ ๐/๐ = ๐๐ ๐๐/๐ = ๐. ๐ ร ๐๐๐๐๐/๐
Es. 0.3
1. ๐ด =๐๐ ๐๐๐
๐ธT๐
2. ๐ฌ๐ = โ๐ธ๐๐ด
๐๐=
๐ฌ๐ท
๐
3. ๐ป = ๐๐ ๐๐
๐ธ๐ด๐ป = ๐๐. ๐ ๐๐๐ ๐๐๐ ๐๐ ; ๐ป = ๐๐๐๐๐ (๐๐๐ ๐๐)
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Capitolo 1
Es. 1.1
1. ๐ = ๐. ๐ ๐๐
2. ๐ฝ = ๐. ๐ยฐ
Es. 1.2
1. ๐ = ๐ ๐ณ
Es. 1.3
1. ๐ญ =๐๐ ๐
๐๐ ๐บ๐๐๐ เท๐๐
2. ๐ฌ๐ป๐ถ๐ป = ๐
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Capitolo 1
Es. 1.4
1. ๐ฌ๐ ๐ =๐
๐๐ ๐บ๐
๐
๐น๐+๐๐๐/๐ เท๐๐, ๐ฌ๐ = ๐, ๐ฌ๐ = ๐
Es. 1.5
1. ๐ฌ๐(๐) =๐
๐๐บ๐๐ โ
๐
๐น๐+๐๐เท๐๐, ๐ฌ๐ = ๐, ๐ฌ๐ = ๐
โข Per ๐ โ ๐ e per ๐น โ โโ๐ฌ+ =๐
๐๐บ๐เท๐๐ ๐ฌโ = โ
๐
๐๐บ๐เท๐๐
Es. 1.6
1. ๐ฌ =๐
๐บ๐เท๐๐ (per ๐ฑ๐ < ๐ < ๐๐)
โข Per ๐ < ๐๐ e per ๐ > ๐๐ โ ๐ฌ = ๐
2. ๐ฌ+ =๐
๐เท๐๐ ๐ฌโ = โ
๐
๐เท๐๐Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 4
Capitolo 1
Es. 1.7
1. ๐ ๐ =๐
๐๐ ๐๐ =
๐๐ฌ
๐๐๐๐, ๐ ๐ = ๐๐ =
๐๐ฌ
๐๐
2. ๐ซ๐ฌ๐ = ๐๐ฌ๐
Es. 1.8
โข ๐ญ๐ = ๐ญ๐ เท๐๐, ๐ญ๐ = ๐. ๐ ร ๐๐โ๐ ๐ต
โข ๐ญ๐ = ๐ญ๐ เท๐๐, ๐ญ๐ = ๐. ๐ ร ๐๐โ๐ ๐ต
โข ๐ญ๐ = โ๐ญ๐เท๐๐, ๐ญ๐ = ๐. ๐ ร ๐๐โ๐ ๐ต
Es. 1.9
โข ๐ญ๐ = โ๐ญ๐ เท๐๐ โ๐ญ๐ เท๐๐, ๐ญ๐ = ๐. ๐ ร ๐๐โ๐๐ต,๐ญ๐ = ๐ ร ๐๐โ๐๐ต
โข ๐ญ๐ = ๐ ร ๐๐โ๐๐ต, ๐ฝ๐ญ๐ = โ๐๐ยฐ
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Capitolo 1
Es. 1.10
โข ๐ญ๐ = ๐ญ๐ เท๐๐ + ๐ญ๐ เท๐๐, ๐ญ๐ = ๐. ๐ ร ๐๐โ๐๐ต,๐ญ๐ = โ๐ ร ๐๐โ๐๐ต
โข ๐ญ๐ = ๐. ๐ ร ๐๐โ๐๐ต, ๐ฝ๐ญ = โ๐๐ยฐ
Es. 1.11
1. ๐ญ๐๐๐ = (โ๐. ๐ ร ๐๐โ๐๐ต)เท๐๐
2. ๐ญ๐๐๐ = ๐. ๐ ร ๐๐โ๐๐ต เท๐๐
Es. 1.12
โข ๐ฌ๐จ = ๐ฌ๐ เท๐๐ + ๐ฌ๐ เท๐๐, ๐ฌ๐ = ๐. ๐ ร ๐๐๐๐ต/๐ช, ๐ฌ๐ = ๐. ๐ ร ๐๐๐๐ต/๐ช
โข ๐ฌ๐จ = ๐. ๐ ร ๐๐๐๐ต/๐ช, ๐ฝ๐ญ = ๐๐ยฐ
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Capitolo 1
Es. 1.13
1. ๐๐ = ๐. ๐ ร ๐๐โ๐๐ช, ๐๐ = ๐. ๐ ร ๐๐โ๐๐ช
Es. 1.14
1. ๐ฌ๐ท(๐) =๐๐
๐๐ ๐บ๐๐เท๐๐
Es. 1.15
1. ๐ธ๐/๐ = ๐ ร ๐๐โ๐๐๐ช
2. ๐ฌ๐ถ = โ๐จ
๐๐บ๐๐นเท๐๐
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Capitolo 1
Es. 1.16
1. ๐ฌ ๐ = โ๐
๐๐ ๐บ๐
๐
๐ ๐+๐ณเท๐๐
Es. 1.17
โข ๐ฌ๐ท = โ๐ฌ๐ เท๐๐ โ ๐ฌ๐ เท๐๐, ๐ฌ๐ท = ๐๐. ๐ ๐ต/๐ช, ๐ฝ๐ญ = โ๐๐ยฐ
Es. 1.18
1. ๐ฌ ๐ =๐
๐๐ ๐บ๐๐๐๐๐๐ เท๐๐
2. ๐ฌ ๐ ๐ณโโ =๐
๐๐ ๐บ๐๐เท๐๐, ๐ฌ ๐ ๐ณโ๐ =
๐๐ณ
๐๐ ๐บ๐๐๐ เท๐๐
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Capitolo 2
Es. 2.1
1. ๐ฝ๐ช =๐ ๐ ๐
๐๐ ๐บ๐๐
Es. 2.2
1. ๐ผ๐ ๐๐๐๐๐๐๐ =๐๐๐
๐๐ ๐บ๐๐
2. ๐พ = ๐ผ๐ ๐๐ = ๐๐๐ฝ๐ช =๐ ๐๐๐๐
๐๐ ๐บ๐๐
Es. 2.3
1. ๐ฝ ๐ =๐
๐๐ ๐บ๐
๐
๐น๐+๐๐, ๐ฌ๐ ๐ = โ
๐๐ฝ
๐๐เท๐๐
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Capitolo 2
Es. 2.4
1. ๐ฝ ๐ =๐
๐๐บ๐๐น๐ + ๐๐ โ ๐ , ๐ฌ๐ ๐ = โ
๐๐ฝ
๐๐เท๐๐
Es. 2.5
1. ๐ซ๐ = ๐๐ โ ๐ฝ ๐ =๐
๐บ๐(๐ โ ๐๐) =
๐
๐บ๐๐
Es. 2.6
1. ๐ฝ๐ช = ๐๐๐ ๐ฝ
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Capitolo 2
Es. 2.7
1. ๐ฝ ๐ =๐
๐๐ ๐บ๐๐๐
๐ณ+ ๐ณ๐+๐ ๐
๐
Es. 2.8
1. ๐พ๐๐๐ =๐๐
๐๐ ๐บ๐๐๐ โ ๐
Es. 2.9
1. ๐ = ๐๐๐๐๐/๐
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Capitolo 2
Es. 2.10
1. ๐พ = ๐. ๐๐ ๐๐ฑ
Es. 2.11
1. ๐ฝ ๐ < ๐น = โ๐๐๐
๐๐บ๐= โ
๐๐๐
๐๐ ๐บ๐๐น๐
2. ๐ฝ ๐ < ๐น =๐
๐๐บ๐๐๐น๐ โ ๐๐ =
๐
๐๐ ๐บ๐๐น๐ ๐๐น๐ โ ๐๐
Es. 2.12
1. ๐ฝ ๐ /๐ = โ๐๐๐ ๐ฝ
2. ๐ฝ๐บ๐ = ๐๐๐๐ ๐ฝ, ๐ฝ๐บ๐ = โ๐๐๐๐ ๐ฝ
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Capitolo 2
Es. 2.13
1. ๐น = ๐๐ ๐๐
2. ๐ธ = ๐๐ ๐๐ช
Es. 2.14
1. ๐ซE๐ = ๐๐ฌ๐ = ๐. ๐ ร ๐๐โ๐๐ ๐ฑ
2. ๐ = ๐. ๐ ร ๐๐๐ ๐/๐
Es. 2.15
1. ๐พ = โ๐. ๐ ร ๐๐โ๐ ๐ฑ
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Capitolo 3
Es. 3.1
1. ๐ฌ ๐ < ๐น = ๐, ๐ฌ ๐ > ๐น =๐
๐๐ ๐บ๐๐๐ เท๐๐ =
๐๐น๐
๐บ๐ ๐๐ เท๐๐
2. ๐ฝ ๐ < ๐น = ๐ฝ ๐น =๐
๐๐ ๐บ๐๐น= ๐๐๐๐๐๐๐๐, ๐ฝ ๐ > ๐น =
๐
๐๐ ๐บ๐๐
Es. 3.2
1. ๐ฌ ๐ > ๐น =๐
๐๐ ๐บ๐๐๐ เท๐๐ =
๐๐น๐
๐ ๐บ๐ ๐๐ เท๐๐, ๐ฌ ๐ < ๐น =
๐ ๐
๐๐ ๐บ๐๐น๐ เท๐๐ =
๐๐
๐ ๐บ๐เท๐๐
2. ๐ฝ ๐ > ๐น =๐
๐๐ ๐บ๐๐, ๐ฝ ๐ < ๐น =
๐
๐๐ ๐บ๐๐น๐ โ
๐๐
๐น๐=
๐
๐๐บ๐๐๐น๐ โ ๐๐
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Capitolo 3
Es. 3.3
1. ๐ฌ ๐ =๐
๐๐ ๐บ๐๐เท๐๐
2. ๐ฝ ๐๐ โ ๐ฝ ๐๐ =๐
๐๐ ๐บ๐๐๐
๐๐
๐๐
Es. 3.4
1. ๐ฌ ๐ > ๐ =๐
๐๐บ๐เท๐๐, ๐ฌ ๐ < ๐ = โ
๐
๐๐บ๐เท๐๐
2. ๐ฝ ๐๐ โ ๐ฝ ๐๐ =๐
๐๐บ๐๐๐ โ ๐๐
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Capitolo 3
Es. 3.5
1. ๐ฌ๐๐๐ = ๐. ๐ ร ๐๐๐ ๐ฝ/๐, ๐ฌ๐๐๐ = ๐ ร ๐๐๐ ๐ฝ/๐
2. ๐ฝ ๐ = โ๐๐๐๐ ๐ฝ
Es. 3.6
1. ๐ฌ ๐ < ๐ = ๐, ๐ฌ ๐ < ๐ < ๐ =๐(๐๐โ๐๐)
๐๐บ๐๐๐ เท๐๐, ๐ฌ ๐ > ๐ =
๐(๐๐โ๐๐)
๐๐บ๐๐๐ เท๐๐
2. ๐ฌ ๐ = ๐๐๐๐ ๐ฝ/๐, ๐ฌ ๐ = ๐๐๐๐ ๐ฝ/๐
Es. 3.7
1. ๐ฝ = โ๐๐๐๐ ๐ฝ
2. ๐พ = ๐๐๐๐ฑ
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Capitolo 3
Es. 3.8
1. ๐ = ๐ ๐๐ช/๐
Es. 3.9
1. ๐ฝ๐ ๐ฌ = ๐. ๐ ๐ต๐๐/๐ช, ๐ฝ๐ ๐ฌ = ๐๐. ๐ ๐ต๐๐/๐ช
2. ๐ช๐ = ๐๐ ๐๐ช, ๐๐ = ๐๐๐ ๐๐ช
Es. 3.10
1. ๐ฌ๐ = ๐. ๐๐ โ ๐๐๐ ๐ฝ/๐, ๐ฌ๐ = โ๐. ๐ โ ๐๐๐ ๐ฝ/๐
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Capitolo 3
Es. 3.11
1. ๐๐ = ๐๐. ๐ ๐๐
2. ๐ = ๐. ๐๐ ๐/๐
Es. 3.12
1. ๐ฌ๐๐๐ = ๐. ๐ โ ๐๐โ๐๐ ๐ฑ = ๐๐. ๐ ๐๐ฝ
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Capitolo 4
Es. 4.1
1. ๐๐ = ๐๐น๐
๐น๐+๐น๐, ๐๐ = ๐
๐น๐
๐น๐+๐น๐
Es. 4.2
1. ๐ช = ๐๐ ๐บ๐๐น๐
2. ๐ช = ๐. ๐๐ ๐๐ญ
Es. 4.3
1. ๐ช =๐บ๐๐บ
๐
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Capitolo 4
Es. 4.4
1. ๐ช = ๐๐ ๐บ๐๐ / ๐๐ ๐น๐/๐น๐
Es. 4.5
1. ๐ช๐ = ๐๐๐ ๐๐ญ, ๐ช๐ = ๐๐๐ ๐๐ญ, ๐ช๐ = ๐๐๐ ๐๐ญ
Es. 4.6
1. ๐ฝ๐ =๐๐
๐บ๐๐ ๐ โ
๐
๐
๐โ๐
๐
2.๐
๐ช๐๐=
๐โ๐
๐บ๐๐บ+
๐
๐บ๐ ๐ค ๐บ
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Capitolo 4
Es. 4.7
1. .
a) ๐ซ ๐ =๐
๐๐ ๐๐เท๐๐
b) ๐ฌ ๐ =๐
๐ ๐ ๐บ๐ ๐ ๐ ๐เท๐๐
c) ๐ท ๐ =๐โ๐
๐
๐
๐๐ ๐๐เท๐๐
2. ๐๐ท = โ๐โ๐
๐๐
Es. 4.8
1. ๐ญ = ๐. ๐ โ ๐๐โ๐๐ต
2. ๐พ = ๐. ๐๐ โ ๐๐โ๐๐ฑ
3. ๐ผ๐ = ๐. ๐๐ โ ๐๐โ๐๐ฑ
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Capitolo 4
Es. 4.9
1. ๐๐ฝ = ๐. ๐ ๐ฝ
Es. 4.10
2. ๐ธ๐ = โ๐ ๐๐ช, ๐ธ๐ = ๐ ๐๐ช, ๐ธ = ๐ ๐๐ช
3. ๐ฝ ๐น๐ = ๐๐๐ ๐ฝ
Es. 4.11
1. ๐๐๐๐๐๐ ๐น๐ = ๐, ๐๐๐๐๐๐๐ ๐น๐ = ๐, ๐๐๐๐๐๐๐ ๐น๐ = ๐๐ ๐๐ช
2. ๐๐๐๐๐๐๐ ๐น๐ = โ๐๐ ๐๐ช, ๐๐๐๐๐๐๐ ๐น๐ = ๐๐ ๐๐ช
3. ๐ซ๐ = ๐๐๐๐ ๐
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Capitolo 4
Es. 4.12
1. ๐ธ๐ = โ๐ ๐๐ช,๐ธ๐ = ๐ ๐๐ช
2. ๐ท๐๐ ๐ < ๐น๐: ๐ฌ ๐ =๐ธ
๐๐ ๐บ๐๐๐
๐ท๐๐ ๐น๐ < ๐ < ๐น๐: ๐ฌ = ๐
๐ท๐๐ ๐ > ๐น๐: ๐ฌ ๐ =๐ธ๐
๐๐ ๐บ๐๐๐
3. ๐ฝ ๐น๐ฉ = ๐๐๐ ๐ฝ, ๐ฝ ๐น๐จ = ๐๐๐ ๐ฝ
Es. 4.13
1. ๐ท๐๐ ๐ < ๐น๐: ๐ฌ = ๐
๐ท๐๐ ๐น๐ < ๐ < ๐น๐: ๐ฌ ๐ =๐ธ
๐๐ ๐บ๐๐๐
๐ท๐๐ ๐น๐ < ๐ < ๐น๐: ๐ฌ = ๐
๐ท๐๐ ๐ > ๐น๐: ๐ฌ ๐ =๐ธ
๐๐ ๐บ๐๐๐
2. ๐ธ๐ = ๐๐ ๐๐ช3. ๐ธ๐ = ๐๐ ๐๐ช, ๐ธ๐ = โ๐๐ ๐๐ช, ๐ธ๐ = ๐๐ ๐๐ช4. ๐ฝ ๐น๐ = ๐๐๐ ๐ฝ
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Capitolo 4
Es. 4.14
1. ๐ธ = ๐. ๐ ๐๐ช
2. ๐ธโฒ = ๐. ๐ ๐๐ช
3. ๐ธ๐ = โ๐. ๐ ๐๐ช
4. ๐ฝ ๐ท๐ = โ๐๐๐ ๐ฝ
Es. 4.15
1. ๐๐ = ๐๐ = ๐๐ = ๐ ๐๐ช, ๐๐ = ๐๐ = โ๐ ๐๐ช
3. ๐ซ๐๐,๐ = ๐๐๐๐ ๐ฝ
4. ๐ผ๐ = ๐. ๐ ๐๐ฑ
5. ๐ผ๐โฒ = ๐. ๐ ๐๐ฑ
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Capitolo 4
Es. 4.16
1. ๐ธ = ๐ ๐๐ช, ๐ธโฒ = ๐. ๐ ๐๐ช
2. ๐ท๐๐ ๐ < ๐น๐ ๐ฌ = ๐, ๐ท๐๐ ๐ โฅ ๐น๐ ๐ฌ ๐ =๐ธโฒ
๐๐ ๐บ๐๐๐
3. ๐ฝ =๐ธโฒ
๐๐ ๐บ๐๐น๐= ๐๐๐ ๐ฝ
Es. 4.17
1. ๐ท๐๐ ๐ < ๐น ๐ฌ ๐ =๐ธ๐
๐๐ ๐บ๐๐๐น๐ =
๐๐
๐๐บ๐๐, ๐ท๐๐ ๐ โฅ ๐น ๐ฌ ๐ = ๐
๐ท๐๐ ๐ < ๐น ๐ฝ ๐ =๐ธ
๐๐ ๐บ๐๐๐น๐๐น๐ โ ๐๐ =
๐๐
๐๐บ๐๐๐น๐ โ ๐๐ ,
๐ท๐๐ ๐ โฅ ๐น ๐ฝ ๐ = ๐
2. ๐๐ =๐ธ
๐๐ ๐น๐(๐๐๐๐๐๐๐๐ ๐๐ ๐ธ ๐๐๐๐๐๐๐๐)
3. ๐๐ท =๐โ๐
๐
๐ธ
๐๐ ๐น๐
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Capitolo 4
Es. 4.18
1. ๐ท๐๐ ๐ < ๐น๐: ๐ฌ = ๐
๐ท๐๐ ๐น๐ < ๐ < ๐น๐: ๐ฌ ๐ =๐ธ
๐๐ ๐บ๐๐๐
๐ท๐๐ ๐น๐ < ๐ < ๐น๐: ๐ฌ ๐ =๐ธ
๐๐ ๐บ๐๐ ๐๐
๐ท๐๐ ๐ > ๐น๐: ๐ฌ ๐ =๐ธ
๐๐ ๐บ๐๐๐
2. ๐ผ๐ = ๐. ๐ โ ๐๐๐ ๐ฑ
Es. 4.19
1. ๐ธ๐ = ๐ธ๐ = ๐. ๐ ๐๐ช, ๐ธ๐ = ๐ ๐๐ช
2. ๐ซ๐๐ = ๐๐ ๐ฝ, ๐ซ๐ฝ๐ = ๐๐ ๐ฝ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 26
Capitolo 4
Es. 4.20
1. ๐ธ๐,๐ = ๐. ๐ ๐๐ช, ๐ธ๐,๐ = ๐๐. ๐ ๐๐ช, ๐ธ๐,๐ป๐ถ๐ป = ๐๐ ๐๐ช
2. ๐ซ๐โฒ = ๐๐. ๐ ๐ฝ
3. ๐ผ๐ญ = ๐. ๐๐ ๐๐ฑ
Es. 4.21
1. ๐ช๐ = ๐๐ ๐๐ญ
2. ๐๐ท = ๐ ๐๐ช
3. ๐ธ = ๐ ๐๐ช
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 27
Capitolo 4
Es. 4.22
1. ๐ช๐๐ = ๐๐. ๐ ๐๐ญ
2. ๐ค = ๐
3. ๐ฌ = ๐ โ ๐๐๐๐ฝ
๐
4. ๐ซ๐ฝ = ๐๐,๐ฝ = ๐. ๐๐ ๐๐ช/๐๐, ๐๐ = ๐๐,๐ซ = ๐. ๐ ๐๐ช/๐๐
Es. 4.23
1. ๐ = ๐๐
2. ๐พ = ๐๐ ๐๐ฑ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 28
Capitolo 4
Es. 4.24
1. ๐ธ = ๐๐. ๐ ๐๐ช
2. ๐ช๐๐ = ๐๐๐ ๐๐ญ
3. ๐ฌ๐ = ๐. ๐ โ ๐๐๐ ๐ฝ/๐, ๐ฌ๐ = ๐. ๐ โ ๐๐๐ ๐ฝ/๐, ๐ฌ๐๐๐ = ๐
Es. 4.25
1. ๐๐ = ๐. ๐๐ ๐๐ช/๐๐, ๐๐ = ๐. ๐ ๐๐ช/๐๐
2. ๐ฌ๐ = ๐. ๐ โ ๐๐๐ ๐ฝ/๐, ๐ฌ๐ = ๐. ๐ โ ๐๐๐ ๐ฝ/๐
3. ๐ฌ๐ = ๐ โ ๐๐๐๐ฝ
๐, ๐ฌ๐ = ๐. ๐ โ ๐๐๐ ๐ฝ/๐,
๐ซ๐ = ๐. ๐๐C
๐๐ , ๐ซ๐ = ๐. ๐ ๐๐ช/๐๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 29
Capitolo 4
Es. 4.26
1. ๐ช๐ = ๐. ๐๐ ๐๐ญ, ๐ช๐๐ = ๐๐. ๐ ๐๐ญ
2. ๐ฌ๐ = ๐ โ ๐๐๐๐ฝ
๐, ๐ฌ๐ = ๐. ๐ โ ๐๐๐ ๐ฝ/๐
3. ๐๐ท๐ = โ๐. ๐๐ ๐๐ช /๐๐, ๐๐ท๐ = ๐. ๐๐ ๐๐ช /๐๐
Es. 4.27
1. ๐ช๐๐ = ๐๐๐ ๐๐ญ
2. ๐ผ๐ = ๐. ๐๐ ๐๐ฑ,๐ผ๐ = ๐. ๐๐ ๐๐ฑ
3. ๐ธ๐ = ๐. ๐๐ ๐๐ช, ๐ธ๐ = ๐. ๐๐ ๐๐ช
4. ๐ฌ๐ = ๐ฌ๐ = ๐๐๐ ๐ฝ/๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 30
Capitolo 4
Es. 4.28
1. ๐๐ = โ๐. ๐ ๐๐ช /๐๐, ๐๐ = ๐. ๐๐ ๐๐ช /๐๐
๐ฌ๐ = ๐๐๐๐ ๐ฝ/๐, ๐ฌ๐ = ๐๐๐๐ ๐ฝ/๐
2. ๐๐ฝ = ๐๐ ๐ฝ
3. ๐๐ท = ๐. ๐๐ ๐๐ช
Es. 4.29
1. ๐ซ๐ = ๐. ๐๐ ๐๐ช
2. ๐ซ๐๐โฒ = ๐๐๐ ๐ฝ
3. ๐พ๐๐๐ = ๐๐ ๐๐ฑ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 31
Capitolo 4
Es. 4.30
2. ๐ = ๐
3. ๐๐ท๐ = โ๐๐ ๐๐ช /๐๐, ๐๐ = ๐. ๐ ๐๐ช /๐๐
4. ๐ฝ ๐ = ๐๐ ๐ฝ
Es. 4.31
2. ๐ธ = ๐ ๐๐ช
3. ๐ = ๐
4. ๐ซ๐ = ๐๐ ๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 32
Capitolo 5
Es. 5.1
1. ๐ = ๐. ๐๐ โ ๐๐โ๐ ๐/๐
Es. 5.2
1. ๐ = ๐. ๐๐ โ ๐๐โ๐ ๐ฝ/๐
2. ๐ = ๐. ๐ โ ๐๐โ๐๐๐, ๐ = ๐. ๐๐ โ ๐๐โ๐ ๐ฆ
Es. 5.3
1. ๐น๐๐ = ๐. ๐ ๐
2. ๐ท = ๐๐๐พ
3. ๐ซV = ๐. ๐ ๐ฝ
4. ๐๐ = ๐. ๐ ๐จ, ๐๐ = ๐. ๐ ๐จ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 33
Capitolo 5
Es. 5.4
1. ๐ฝ๐ซ๐ฉ = ๐๐ ๐ฝ
2. ๐ฝ๐ช๐ซ = ๐๐ ๐ฝ
3. ๐ฝ๐จ๐ช = ๐๐ ๐ฝ
4. ๐ฝ๐จ๐ฉ = ๐๐ ๐ฝ
Es. 5.5
1. ๐ = ๐. ๐๐๐ ๐๐ฆ
Es. 5.6
1. ๐ = ๐๐ ๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 34
Capitolo 5
Es. 5.7
1. ๐ = ๐. ๐๐ ๐
Es. 5.8
1. ๐ฐ = ๐ฑ๐๐บ/๐
Es. 5.9
1. ๐ = ๐. ๐๐ ๐ค๐
2. ๐๐ฉ๐๐ฌ๐ = ๐. ๐๐ ๐๐ฎ๐ซ๐จ
Es. 5.10
1. ๐ฅ = ๐. ๐๐ ๐ฆ
2. ๐โฒ = ๐๐. ๐ ๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 35
Capitolo 5
Es. 5.11
1. ๐พ๐ = ๐๐. ๐ ๐๐ฑ
Es. 5.12
1. ๐ = ๐ ๐
Es. 5.13
1. ๐ = ๐. ๐ โ ๐๐๐๐จ /๐๐
2. ๐ฌ = ๐. ๐๐๐ ๐ฝ/๐
3. ๐ซ๐ = ๐๐ ๐
4. ๐ท = ๐๐๐๐พ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 36
Capitolo 6
Es. 6.1
1. ๐ญ๐น = ๐๐๐น๐ฉ เท๐๐, ๐ญ๐ช = โ๐๐๐น๐ฉ เท๐๐ โ ๐ญ๐ป๐ถ๐ป = ๐
Es. 6.2
1. ๐ = ๐. ๐ โ ๐๐๐ ๐/๐
2. ๐ฉ = ๐. ๐ โ ๐๐โ๐ ๐ป
Es. 6.3
1. ๐ฉ = ๐. ๐ โ ๐๐โ๐ ๐ป
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 37
Capitolo 6
Es. 6.4
1. ๐ฉ = ๐. ๐ โ ๐๐โ๐๐ป
Es. 6.5
1. ๐ด = ๐ โ ๐๐โ๐ ๐ต๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 38
Capitolo 7
Es. 7.1
1. ๐ฉ = ๐. ๐ โ ๐๐โ๐ ๐ป
Es. 7.2
1. ๐๐๐ซ ๐ซ > ๐: ๐ฉ(๐) =๐๐ ๐
๐๐ ๐
๐๐๐ซ ๐ซ < ๐: ๐ฉ(๐) =๐๐ ๐ ๐
๐ ๐ ๐น๐
Es. 7.3
1. ๐ฉ = ๐๐ ๐ ๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 39
Capitolo 7
Es. 7.4
1. ๐ฉ ๐ =๐๐ ๐ต ๐
๐๐ ๐
Es. 7.5
1. ๐ฉ ๐ = ๐ โ ๐๐โ๐ ๐ป
Es. 7.6
1. ๐ฉ๐ป๐ถ๐ป = ๐ โ ๐๐โ๐ ๐ป diretto lungo asse x positivo
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 40
Capitolo 7
Es. 7.7
1. ๐ = ๐. ๐ ๐จ
Es. 7.8
1. ๐ = ๐. ๐ ๐๐
Es. 7.9
1. ๐ฉ ๐ =๐๐๐ฐ
๐๐ ๐
2. ๐ญ = โ๐๐โ๐ ๐ต
3. ๐ฝ ๐ฉ = ๐. ๐ ร ๐๐โ๐ ๐พ๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 41
Capitolo 7
Es. 7.10
1. ๐ป๐๐๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐
2. ๐ญ๐ = ๐ ร ๐๐โ๐๐ ๐ต, diretta lungo asse z negativo
3. ๐น = ๐. ๐ ร ๐๐โ๐ ๐
4. ๐ป = ๐. ๐๐ ร ๐๐โ๐๐ ๐
Es. 7.11
1. ๐ฉ๐ป๐ถ๐ป = ๐. ๐ ร ๐๐โ๐ ๐ป diretto lungo asse y positivo
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 42
Capitolo 8
Es. 8.1
1. ฦ๐ = โ๐๐. ๐ ๐ฝ
Es. 8.2
1. ฦ๐ = โ๐. ๐๐ ๐ฝ
Es. 8.3
1. ๐ฉ = ๐. ๐ โ ๐๐โ๐ ๐ป
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 43
Capitolo 8
Es. 8.4
1. ๐ณ =๐๐๐ต
๐๐
๐ ๐ ๐๐
๐น+๐
๐น
2. ๐ณ๐ = ๐. ๐๐ โ ๐๐โ๐ ๐ฏ/๐
โข ๐ณ๐,๐ = ๐. ๐๐๐๐ ๐ฏ/๐
Es. 8.5
1. ๐ผ๐ =๐๐๐ต
๐๐
๐ ๐ ๐๐
๐น+๐
๐น๐๐ =
๐
๐๐ณ ๐๐
Es. 8.6
1. ๐ด = ๐๐๐๐๐ต๐๐บ๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 44
Capitolo 8
Es. 8.7
1. ฦ๐ = ๐ด๐๐๐ ๐๐๐๐๐, ๐ด =๐๐๐ต๐๐ต๐๐ ๐๐
๐๐๐๐๐ฝ
๐๐๐
Es. 8.8
1. ๐ฉ ๐, ๐ =๐
๐๐๐๐บ๐๐๐ฌ๐๐ ๐๐๐๐๐
2. ฦ๐ =๐
๐๐บโฒ๐ ๐๐๐บ๐๐
๐๐ฌ๐๐โฒ๐๐๐๐๐ = ๐. ๐๐ ๐๐๐๐๐๐๐ ๐ฝ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 45
Capitolo 8
Es. 8.9
1. ๐ญ = ๐ ร ๐๐โ๐๐ ๐ต, diretta verso il basso
2. ๐ซ๐ = ๐๐ ๐, ๐ ๐ > ๐ ๐
Es. 8.10
1. ๐ = ๐ ร ๐๐โ๐ ๐จ
Es. 8.11
1. ๐ = ๐๐ ๐๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 46
Capitolo 8
Es. 8. 12
1. ฦ๐ = ๐ ร ๐๐โ๐ ๐ฝ = ๐๐ ๐๐ฝ
2. ๐ข = ๐ ร ๐๐โ๐๐จ = ๐ ๐๐จ, verso orario
Es. 8.13
1. ๐ = ๐. ๐๐ ๐จ, verso orario
Es. 8.14
1. ๐ฉ ๐ =๐๐๐ฐ
๐๐ ๐
2. ๐ฝ ๐ฉ ๐ =๐๐๐ฐ ๐
๐๐ ๐๐
๐ ๐ +๐
๐ ๐
3. ๐ = ๐ ร ๐๐โ๐ ๐จ = ๐๐ ๐๐จ, verso orario
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 47
Capitolo 8
Es. 8. 15
1. ๐ ๐ = ๐๐
2. ๐ฑ ๐ฉ(๐) = ๐ฉ๐๐๐ ๐ +
๐
๐๐๐๐ + ๐
3. ๐ = โ๐ ร ๐๐โ๐ ๐จ, verso antiorario
Es. 8.16
1. ๐๐๐๐ = ๐. ๐๐ ๐, ฦ๐,๐๐๐ = ๐. ๐๐ ๐ฝ
2. ๐น = ๐๐๐๐ ๐ด, ๐๐๐๐ = ๐. ๐ ๐๐จ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 48
Capitolo 8
Es. 8. 17
1. ฦ๐, = ๐. ๐๐ ๐ฝ
2. ๐ = ๐๐๐จ, verso antiorario
3. ฦ๐, = ๐
Es. 8.18
1. ฦ๐, = โ๐๐ ๐ ๐ฐ๐๐ต
๐ ๐ ๐๐๐
๐+๐
๐๐โ๐/๐, ๐ = ฦ๐, /๐น, verso orario
2. ๐ฌ = ๐. ๐ ร ๐๐โ๐๐ ๐ฑ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 49
Esercizi riepilogo
Es. R.1
1. ๐๐ = ๐. ๐๐ ๐๐จ, ๐๐ฉ = ๐
2. ๐ซ๐ฝ = ๐. ๐๐ ๐๐พ๐
3. ๐ = ๐๐. ๐ ๐๐ช
Es. R.2
1. ๐ฉ = ๐. ๐ โ ๐๐โ๐ ๐ป
Es. R.3
1. ๐๐๐๐ = ๐ ๐จ
2. ๐ฌ๐๐๐ = ๐๐๐ฑ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 50
Esercizi riepilogo
Es. R.4
1. ๐ฉ๐
๐= ๐. ๐ โ ๐๐โ๐ ๐ป
2. ๐ฉ๐ซ
๐= ๐. ๐ โ ๐๐โ๐ ๐ป
3. ๐ฝ๐ = ๐๐ ๐๐พ๐/๐
Es. R.5
1. ๐ = ๐. ๐ ๐/๐
2. ๐ท = ๐. ๐๐๐พ
Es. R.6
1. ๐ = ๐. ๐๐ ๐๐จ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 51
Esercizi riepilogo
Es. R.7
1. ๐ฉ๐จ = โ๐ โ ๐๐โ๐ ๐ป
2. ๐ญ๐ = ๐. ๐ ๐ต/๐
3. ๐น = ๐. ๐ ๐
4. ๐ธ = ๐. ๐ ๐๐ช
Es. R.8
1. ๐ = ๐. ๐๐ ๐/๐
2. ๐ญ = โ๐. ๐๐๐ ๐ต
3. ๐ธ = ๐๐. ๐ ๐๐ช
4. ๐พ = ๐. ๐ ๐๐ฑ
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 52
Esercizi riepilogo
Es. R.9
1. ๐ญ = ๐๐๐ต
Es. R.10
1. ๐ณ๐ =๐๐
๐ ๐ ๐๐
๐น๐
๐น๐
๐ผ๐,๐ =๐๐
๐ ๐ ๐๐
๐น๐
๐น๐๐๐
Elisabetta Bissaldi (Politecnico di Bari) - A.A. 2020-2021 53