Calculus Archive: Questions from May 12, 2023
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4. Find the description in polar coordinates of these regions. The description must be in the form R: 0min 00max Tmin <r<Tmax (a) The region enclosed by the circle x² + y² = 25. (b) The region
4. Hallar la descripción en coordenadas polares de estas regiones. La descripción debe estar en la forma \[ R:\left\{\begin{array}{l} \theta_{\min } \leq \theta \leq \theta_{\max } \\ r_{\min } \leq2 answers -
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Find a particular solution: \[ \mathbf{y}^{\prime}=\left[\begin{array}{cc} -6 & -3 \\ 1 & -2 \end{array}\right] \mathbf{y},+\left[\begin{array}{l} 4 e^{-3 t} \\ 4 e^{-5 t} \end{array}\right] \]2 answers -
-18 Evaluate the triple integral. 9. \( \iiint_{E} y d V \), where \[ E=\{(x, y, z) \mid 0 \leqslant x \leqslant 3,0 \leqslant y \leqslant x, x-y \leqslant z \leqslant x+y\} \]2 answers -
evaluate the triple integral
\( \iiint_{E} e^{z / y} d V \), where \[ E=\{(x, y, z) \mid 0 \leqslant y \leqslant 1, y \leqslant x \leqslant 1,0 \leqslant z \leqslant x y\} \]2 answers -
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Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=3-z^{2}, \quad 0 \leq x, z \leq 5 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
1. \( \iiint_{E} 2 x d V \), where \[ E=\left\{(x, y, z) \mid 0 \leqslant y \leqslant 2,0 \leqslant x \leqslant \sqrt{4-y^{2}}, 0 \leqslant z \leqslant y\right\} \]0 answers -
15.1 Calculate the double integral
28. \( \iint_{R}\left(y+x y^{-2}\right) d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 2,1 \leqslant y \leqslant 2\} \)2 answers -
\( f(x, y)=\left\{\begin{array}{ll}\frac{x^{2} y^{3}}{2 x^{2}+y^{2}} & \text { if }(x, y) \neq(0,0) \\ 1 & \text { if }(x, y)=(0,0)\end{array}\right. \)2 answers -
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Match each expression with an equivalent one. In this question \( x, y>1 \). \[ \begin{array}{lll} y=x & x^{y}=3 & y=e^{x} \\ e^{x-y}=3 & y=3^{x} & e^{y}=\frac{e^{x}}{e^{3}} \end{array} \] 1. \( y=x-\2 answers -
el que me pueda ayudar con estos ejercicio estare total agradecido.
Ejercicios Calcul 1 (1) Hallar los valoris máximo y mÃnimo locales de; \( f(x)=3 x^{4}-4 x^{3}-12 x^{2}+5 \) (a) mÃnimo -24 y \( 36 j \) máximo 72 (b) mÃnimo 36 y 72 j máximo -24 (1) minimo \( -2 answers -
Given \( f(x, y)=3 x^{5}-2 x y^{6}-6 y^{4} \), \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \]2 answers -
Given \( f(x, y)=-4 x^{4}+6 x y^{5}-5 y^{2} \), find the following numerical values: \[ f_{x}(3,2)= \] \[ f_{y}(3,2)= \]2 answers -
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11-14 Evaluate the double integral. 11. \( \iint_{D} \frac{y}{x^{2}+1} d A, \quad D=\{(x, y) \mid 0 \leqslant x \leqslant 4,0 \leqslant y \leqslant \sqrt{x}\} \) 12. \( \iint_{D}(2 x+y) d A, \quad D=\2 answers -
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