Advanced Math Archive: Questions from September 23, 2022
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Un contenedor rectangutar de aimacenamiento sin tapa ha de tener un volumen de \( 10 \mathrm{~m}^{3} \). La longhud de su base es dos veces el ancho. El material para la base cuesta s1o por metro cuad1 answer -
Your answer is CORRECT. Find the general solution of \[ y^{\prime}=\frac{3 x^{4} e^{y / x}+x^{2} y^{2}}{x^{3} y} . \] a) \( \quad y=x \ln \left(\frac{C x-x \ln \left(x^{3}\right)}{x+y}\right) \) b) \(1 answer -
Show if the following functions are coercive or not. a \( f(x, y)=4 x^{2}+2 x y+2 y^{2} \). b \( f(x, y)=2 x^{2}-8 x y+y^{2} \) c \( f(x, y, z)=x^{3}+y^{3}+z^{3} \). \( \mathbf{d} f(x, y)=x^{2}-2 x y^3 answers -
Find the general solution of \[ y^{\prime}=\frac{y+\sqrt{x^{2}-y^{2}}}{x} \] Answer: \( y=x \sin (\ln x+C) \)1 answer -
Lots of details please so i can figure out what i'm doing wrong!
Compute the gradient vector fields of the following functions: A. \( f(x, y)=8 x^{2}+5 y^{2} \) \( \nabla f(x, y)=\mathbf{i}+\mathbf{j} \) B. \( f(x, y)=x^{5} y^{5} \), \( \nabla f(x, y)=\quad \) i+ \1 answer -
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Part 2 A and B Part 3
Evalúe el integral camblando a coordenadas polares a) \( \int_{-1}^{1} \int_{0}^{\sqrt{1-x^{2}}} \cos \left(x^{2}+y^{2}\right) d y d x \) b) \( \int_{0}^{3} \int_{0}^{\sqrt{9-x^{2}}}\left(x^{2}+y^{2}1 answer -
Homework 2.11. Find the solution of the following initial value problems 1. \( y^{\prime \prime}+2 y^{\prime}-15 y=e^{3 x}, y(0)=y^{\prime}(0)=1 \) 2. \( y^{\prime \prime}-4 y=e^{x}, y(0)=y^{\prime}(01 answer -
Consider the parametrization of the unit circle: \( \gamma=e^{i t}, 0 \leq t \leq 2 \pi \). Compute (i) \( \int_{\gamma} \frac{e^{z}}{z} d z \), (ii) \( \int_{\gamma} \frac{z^{3}}{z^{2}+4} d z \).1 answer