Calculo 2
Por: felipeguerra • 31/3/2015 • Trabalho acadêmico • 1.329 Palavras (6 Páginas) • 251 Visualizações
FACULDADE ANHANGUERA |
Trabalho de Calculo 2 |
3° Período de Engenharia Mecânica |
Felipe J. Ribeiro Guerra |
06/03/2015 |
01. Encontre a equação da reta tangente que toca ponto indicado para a função:
a) 𝑦 = 9 − 𝑥 ² ; 𝑃(−3, 0)
Y = f(x) = 9 – x²
F(x₁ + ∆x) = 9 – (x₁ + ∆x)²
F(x₁ + ∆x) = 9 – [(x₁ ²+2x₁∆x +(∆x )²]
F(x₁ + ∆x) = 9 – x₁ ² – 2x₁∆x – (∆x )²
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[pic 5]
[pic 6][pic 7][pic 8][pic 9]
[pic 10]
y₂ - y₁ = [pic 11]
y₂ 0 = 6[[pic 12][pic 13]
y₂ = 6[pic 14]
y₂ = 6[pic 15]
y = 6x + 18
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b) 𝑦 = 𝑥³ + 1; 𝑃(−2, -7)
Y = f(x) = 𝑥³ + 1
F(x₁ + ∆x) = (x₁ + ∆x)³ +1
F(x₁ + ∆x) = (-2 + ∆x)³ +1
F(x₁ + ∆x) = -2³ + 3(-2)²∆x + 3(-2)(∆x)² + (∆x)³ +1
F(x₁ + ∆x) = -7 + 12∆x - 6(∆x)² + (∆x)³
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y₂ - y₁ = [pic 24]
y₂ + 7 = [pic 25]
y₂ = - 7[pic 26]
y = [pic 27]
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c) y =; 𝑄(3, 2)[pic 28]
y = f(x) =; [pic 29]
F(x₁ + ∆x) = [pic 30]
[pic 31]
[pic 32]
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[pic 37]
[pic 38]
[pic 39]
y₂ - y₁ = [pic 40]
y₂ - 2 = [pic 41]
y₂ = [pic 42]
y₂ = [pic 43]
y₂ = [pic 44]
y = [pic 45]
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d) ; P(2,1)[pic 46]
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y₂ - y₁ = [pic 64]
y₂ - 1 = [pic 65]
y₂ = [pic 66]
y₂ = [pic 67]
y = [pic 68]
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e) ; P(3, )[pic 69][pic 70]
[pic 71]
[pic 72]
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[pic 75]
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[pic 78]
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y₂ - y₁ = [pic 82]
y₂ - = [pic 83][pic 84]
y₂ - = [pic 85][pic 86]
y₂ = + [pic 87][pic 88]
y₂ = [pic 89]
y₂ =[pic 90]
y =[pic 91]
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f) y = 3x² - 2x + 5:; P(-1, 10)
F(x₁ + ∆x) =3(-1+∆x)² - 2(-1 +∆x) + 5
F(x₁ + ∆x) =3[(-1)²+ 2(-1)(∆x)+(∆x)² ] +2 - 2∆x + 5
F(x₁ + ∆x) =3 - 6∆x + (∆x)² +7 - 2∆x
F(x₁ + ∆x) =10 - 8∆x + (∆x)²
[pic 92]
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[pic 94]
[pic 95]
[pic 96]
[pic 97]
y₂ - y₁ = [pic 98]
y₂ - 10 = [pic 99]
y₂ - 10 = [pic 100]
y₂ = + 10[pic 101]
y₂ = [pic 102]
y = [pic 103]
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g) y = x³ - 8; P(0, -8)
F(x₁ + ∆x) = (x₁ + ∆x)³ - 8
F(x₁ + ∆x) = x₁³ + 3 x₁²∆x + 3 x₁(∆x)² + (∆x)³ - 8
F(x₁ + ∆x) = 0³ + 3(0)²∆x + 3 (0)(∆x)² + (∆x)³ - 8
F(x₁ + ∆x) = (∆x)³ - 8
[pic 104]
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[pic 109]
y₂ - y₁ = [pic 110]
y₂ + 8 = [pic 111]
y₂ = - 8
y = - 8
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h) ; P (1, 2)[pic 112]
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y₂ - y₁ = [pic 128]
y₂ - 2 = [pic 129]
y₂ = [pic 130]
y₂ = [pic 131]
y= [pic 132]
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; P(-2, -)[pic 133][pic 134]
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y₂ - y₁ = [pic 148]
y₂ -(- ) = [pic 149][pic 150]
y₂ + = [pic 151][pic 152]
y₂ = - [pic 153][pic 154]
y₂ = - [pic 155][pic 156]
y₂ = [pic 157]
y = [pic 158]
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