Calculus Archive: Questions from April 16, 2023
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(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}+36 y^{\prime}=0 \] \[ \begin{array}{l} y(0)=-5, y^{\prime}(0)=30, y^{\prime \prime}(0)=0 . \\ y(x)= \end{array} \]2 answers -
Let \( U(x, y)=x e^{k x y^{2}} \). Determine the function \( p(x, y) \) such that \[ p(x, y) \frac{\partial U}{\partial x}+x \frac{\partial U}{\partial y}-y^{2} U=0 \]2 answers -
Problema: Conteste las siguientes preguntas: a. ¿Cuánto es la longitud de onda (en nm) para una frecuencia de (v) de 5.73 x \( 10^{14} \mathrm{~Hz} \) ? b. ¿Cuál es la región del espectro electro0 answers -
Ejercicios: 1) Halle \( \frac{d y}{d x} \) para \( y=x^{2} \ln \left(\frac{x}{x+3}\right) \) 2) Utilice diferenciación logaritmica para determinar \( \frac{d y}{d x} \) para \( y=\frac{x}{\sqrt{3 x+22 answers -
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Find the solution of the following differential equation
(1) \( y^{\prime \prime}+2 y^{\prime}+y=0 \) (2) \( y^{\prime \prime}+5 y^{\prime}+4 y=0 \) (3) \( y^{\prime \prime}+4 y=0, y(\pi)=0, y^{\prime}(\pi)=1 \) (4) \( y^{\prime \prime}-3 y^{\prime}-4 y=0,2 answers -
i have 4 hours left..
Evaluate the triple integral \( \iiint_{Q} f(x, y, z) d V \). \[ \begin{array}{l} f(x, y, z)=8 x+9 y-10 z, Q=\{(x, y, z) \mid 1 \leq x \leq 3,-8 \leq y \leq 8,0 \leq z \leq 9\} \\ \iiint_{Q} f(x, y, z2 answers -
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If \( R=\{(x, y) \mid 0 \leq x \leq 2 \) and \( 1 \leq y \leq 4\} \), evaluate \[ \int_{R} \int\left(9 x^{2}+3 x y^{3}\right) d A \] The value is2 answers -
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