Advanced Math Archive: Questions from February 16, 2023
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Find out if they exist, the limits in a, b and c. Explain the procedure whether it exists or not.
1. Encontrar si existen, los límites en a, b y c . Explicar el procedimiento a sea si existe ó no. a. \[ \lim _{(x, y) \rightarrow(0,0)} \frac{x^{2} y-y^{3}}{|x|^{3}+|y|^{3}} \] b. \[ \lim _{(x, y)2 answers -
2.consider the funtion: A. Find the plane tangent to the surface at the point (3, 1, 1) B. Find the normal line to the surface in (3, 1, 1)
2. Consideremos la función: \[ f(x, y)=\frac{1}{6}\left(e^{y-1} x^{2}-3 y^{2}\right)=z \] a. Encontrar el plano tangente a la superficie en el punto \( (3,1,1) \) b. Encontrar la recta normal a la su2 answers -
Sea f(x,y)=x3+4x2y−2y y u=��1/3,2√2/3. (I) Find the gradient of f. (Ii) Find the Duf directional derivative (x, y) in (−1, 2) (Iii) Find the direction of the directional derived m'axima o
4. Sea \( f(x, y)=x^{3}+4 x^{2} y-2 y \quad \) y \( \quad u=\langle 1 / 3,2 \sqrt{2} / 3\rangle \). (i) Encontrar el gradiente de \( f \). (ii) Encontrar la derivada direccional \( D_{u} f(x, y) \) en2 answers -
Let's consider the function: F(x,y)= 16(ey−1x2 −3y2)=z A. Find the plane tangent to the surface at the point (3, 1, 1) B. Find the normal line to the surface in (3, 1, 1)
2. Consideremos la función: \[ f(x, y)=\frac{1}{6}\left(e^{y-1} x^{2}-3 y^{2}\right)=z \] a. Encontrar el plano tangente a la superficie en el punto \( (3,1,1) \) b. Encontrar la recta normal a la su2 answers -
Find the m ́aximos and m ́ınimos, and where they are reached, of the function f(x,y)=x2 +y2 +xy {(X, y) : x2 + y2 ≤ 1} (I) Local. (Ii) Absolute. (Iii) Identify the chronic points inside the d
6. Encontrar los máximos y mínimos, y en donde se alcanzan, de la función \[ f(x, y)=x^{2}+y^{2}+x y \] \[ \left\{(x, y): x^{2}+y^{2} \leq 1\right\} \] (i) Locales. (ii) Absolutos. (iii) Identifica2 answers -
2 answers
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2 answers
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match
1. \( L\left\{e^{-7 t}\right\}= \) 2. \( L\{\sin 2 t\}= \) 3. \( L\left\{t^{5}\right\}= \) \( \frac{2}{s^{2}+4} \) \( \frac{1}{s+4} \) \( \frac{\sqrt{3}}{s^{2}+3} \) 4. \( L\{\cos \sqrt{3} t\}= \) 5.2 answers -
Solve the exact differential equation. \[ \begin{array}{l} \left(y^{3}-y^{2} \sin (x)-x\right) d x+\left(3 x y^{2}+2 y \cos (x)\right) d y=0 \\ f(x, y)=x y^{3}+y^{2} \cos (x)-\frac{x^{2}}{2}+c \\ f(x,2 answers -
determine by convolution
-Determine por convolución \[ \mathcal{L}^{-1}\left\{\frac{1}{(S-2)\left(S^{2}-4 S+5\right)}\right\} \]2 answers -
where c is the rectangle (1,0),(2,0),(2,2),(1,2)
-Calcule la integral de línea: \( \int \frac{1}{Z} d Z \) donde \( c \) es el rectángulo \( (1,0),(2,0),(2,2) \) y \( (1,2) \) recordar que \( z=x+y i \) \[ d z=d x+i d y \]2 answers -
2 answers
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2 answers
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2. Find a harmonic conjugate \( v(x, y) \) of \[ u(x, y)=e^{x} \cos y+e^{y} \cos x+2 x y-3 x+4 y+6 \]2 answers -
6. Solve the initial value problem \( y^{\prime \prime}+y=0, \quad y(0)=0, y^{\prime}(0)=3 \). ( 16 pts.)2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For Part of the surface \( x=z^{3} \), where \( 0 \leq x, y \leq 14^{-\frac{3}{2}} ; \quad f(x, y, z)=x \) \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
c) \( y^{\prime \prime}+2 y^{\prime}+2 y=0, y(\pi / 4)=2, y^{\prime}(\pi / 4)=-2 \) d) \( y^{\prime \prime}(t)+2 \cos (\theta) y^{\prime}(t)+y(t)=0, y(0)=2, y^{\prime}(0)=-1 \) e) \( \left.y^{\prime \0 answers -
2 answers
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a,b
2. (a) Supongamos que \( A \neq \emptyset \) está acotado inferiormente. Designemos por \( -A \) el conjunto de todos \( \operatorname{los}-x \) con \( x \) en \( A \). Demostrar que \( -A \neq \empt2 answers -
please help and choose one of the answers below
Simplify the general solution using your Laws of Logarithms. \[ y=c_{1} \ln |x|+c_{2} x \ln |x|+\ln \left|\frac{x}{x+4}\right| \] A) \( y=c_{1} \ln |x|+c_{2} x \ln |x|+\ln |x+4| \) B) \( y=c_{1} \ln |3 answers -
2 answers
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Match each trigonometric ratio correctly. \[ \sin (x) \] \[ \cos (x)= \] \[ \tan (x) \] \[ \sin (y) \] \[ \cos (y) \] \[ \tan (y) \]2 answers -
Find the limit. \[ (x, y) \rightarrow(0,1) \frac{y^{3} \sin x}{x} \] Select one: A. \( \infty \) B. 1 C. 0 D. No limit2 answers -
Find the limit. \[ (x, y) \rightarrow(0,1) \frac{y^{3} \sin x}{x} \] Select one: A. \( \infty \) B. 1 C. 0 D. No limit2 answers -
Calculate \( \iint_{S} f(x, y, z) d S \) For \[ x^{2}+y^{2}=4, \quad 0 \leq z \leq 4 ; \quad f(x, y, z)=e^{-z} \] \[ \iint_{S} f(x, y, z) d S= \]2 answers -
2 answers
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Resolver este problema de valor inicial usando el método de solución de la ecuación de Bernoulli, según discutido en clase. Escribir la respuesta en la forma \( y=f(x) \) completamente simplificad2 answers -
43. Solve the initial value problem: \[ \begin{array}{lc} y^{\prime \prime \prime}-y^{\prime}=0 ; & y(0)=2 \\ y^{\prime}(0)=3, & y^{\prime \prime}(0)=-1 \end{array} \]2 answers