Calculus Archive: Questions from May 07, 2023
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8,18,19,20,24,28,36,50,52
7-46 Find the derivative of the function. 7. \( F(x)=\left(5 x^{6}+2 x^{3}\right)^{4} \) 8. \( F(x)=\left(1+x+x^{2}\right)^{99} \) 9. \( f(x)=\sqrt{5 x+1} \) 10. \( f(x)=\frac{1}{\sqrt[3]{x^{2}-1}} \)2 answers -
\[ \text { If } \mathscr{D}=\left\{(x, y) \mid 1 \leq x \leq 2, x^{2} \leq y \leq 4\right\} \] then:2 answers -
Calculate all four second-order partial derivatives of \( f(x, y)=(2 x+3 y) e^{y} \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
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Additional material: Solve the given initial value problems: (a) \( 9 y^{\prime \prime}-12 y^{\prime}+4 y=0, \quad y(0)=2, \quad y^{\prime}(0)=-1 \); (b) \( y^{\prime \prime}+4 y^{\prime}+4 y=0, \quad2 answers -
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En los ejercicios utilizar el teorema de Green para eva luar la integral de línea. 14. \( \int_{C}\left(x^{2}-y^{2}\right) d x+2 x y d y \) 17. \( \int_{C} \cos y d x+(x y-x \operatorname{sen} y) d y2 answers -
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Evaluate the integral. \[ \int_{-4}^{-1}\left(\frac{y^{6}-8 y}{y^{3}}\right) d y \] \[ \int_{-4}^{-1}\left(\frac{y^{6}-8 y}{y^{3}}\right) d y= \]2 answers -
1.Escriba con notación de sumatoria si \[ S_{s}=1+4+9+16+25 \] 2. Escriba con notación de sumatoria si: \[ S_{4}=1 / 2+1 / 4+1 / 8+1 / 16+1 / 32 \]2 answers -
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4. Encuentra la suma de \( S_{11} \ldots \ldots \). si \( a_{1}=1 / 3 \) y \( a_{2}=1 / 2 \) 5. Encuentra \( a_{1} \ldots . \quad \) Si \( a_{3}=13 \) y \( a_{10}=55 \)2 answers -
6. Marca o dibuja los siguientes puntos (4 ptos cu) a) \( (2, \mathrm{pi} / 2) \) b) \( (3,9 \mathrm{pi} / 4) \)0 answers -
9. Encuentra las coordenadas rectangulares o polares (3 ptos cu) Coord. Rect Coord. polar a) \( (3,4) \) c) \( (1,-1) \)2 answers -
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