Advanced Math Archive: Questions from October 26, 2022
-
solve 6,7,10,11
Solve. 6. \( \left(x^{2} D^{2}-3 x D+4\right) y=x+x^{2} \ln x \) 7. \( \left(x^{2} D^{2}-2 x D+2\right) y=\ln ^{2} x-\ln x^{2} \) Ans. \( y=C_{1} x^{2}+C_{2} x^{2} \ln x+x+\frac{1}{6} x^{2} \ln ^{3} x2 answers -
2 answers
-
2 answers
-
Solve \[ (x+2) \frac{d y}{d x}+y=f(x), \text { where } f(x)=\left\{\begin{array}{ll} 2 x, & 0 \leq x \leq 2, \\ 4, & x>2 \end{array} \quad y(0)=0\right. \]2 answers -
Parte 1: Encuentre las siguientes transformadas de Laplace o transformada inversa de Laplace. 6) \( L^{-1}\left\{\frac{s}{s^{2}-10 s+29}\right\} \) Part 1: Find the following Laplace transform or inv2 answers -
Parte 1: Encuentre las siguientes transformadas de Laplace o transformada inversa de Laplace. 7) \( L^{-1}\left\{\frac{e^{-2 s}}{s^{3}}\right\} \) Part 1: Find the following Laplace transform or inve2 answers -
Parte 1: Encuentre las siguientes transformadas de Laplace o transformada inversa de Laplace. 8) \( L\left\{\int_{0}^{t} \sin 2(t-\tau) \cos 3 \tau d \tau\right\} \) Part 1: Find the following Laplac2 answers -
Parte 2: Resuelve el problema de valor inicial usando el método de transformada de Laplace.(10 ptos) 1) \( y^{\prime \prime}+6 y^{\prime}+4 y=0, y(0)=1, y^{\prime}(0)=0 \) Part 2: Solve the initial2 answers -
2 answers
-
Solve the following initial value problem. \[ y^{\prime \prime \prime}-4 y^{\prime \prime}+y^{\prime}+6 y=0 ; \quad y(0)=-1, \quad y^{\prime}(0)=3, \quad y^{\prime \prime}(0)=-3 \]2 answers -
Given the equation x 2/4 + Y 2/9 +z 2/36=1 a. Identify the graphic b. complete the following graphic c. Plot the equation
4. Dada la ecuación \( \frac{x^{2}}{4}+\frac{y^{2}}{9}+\frac{z^{2}}{36}=1 \) a. Identifique la gráfica b. Complete la siguiente tabla: \( \mathrm{C} \) Frafinst la amsanicin0 answers -
Complex numbers Exercice:
3. Sigui \( f(x, y)=e^{x} \cdot \sin y \). Verifica que: \( \frac{\partial^{2} f}{\partial x^{2}}+\frac{\partial^{2} f}{\partial y^{2}}=0 \) 4. Sigui \( f(x, y)=x e^{y^{2}}+y \ln x \). Verifica que: \2 answers -
1. \( \frac{x-2}{2 y+1} d x-\frac{3 x+1}{y+2} d y=0 \). 2. \( x \frac{d y}{d x}-(2 x+1) y=x^{3} \) 3. \( \frac{d y}{d x}=\frac{y}{x}+\tan ^{2} \frac{y}{x}+1 \) 4. \( x y^{\prime}-y+2 \sqrt{y}=0 ; \qua2 answers -
Find the general solution of the differential equation \( y^{\prime \prime}+4 y^{\prime}+3 y=20 \cos x \). You can use undertermined coefficient \[ \begin{array}{l} y=k_{1} e^{3 x}+k_{2} e^{x}+4 \sin2 answers -
0 answers
-
Numerical Analysis question: Consider the sequence un+1 = un +1/2(1−u2n) and initial term u0 = 0. P-2.1 Prove that for any n ∈ N there is a ∈ [0, 1]. P-2.2 Prove that the sequence is monotonical
Considere la sucesión \( u_{n+1}=u_{n}+\frac{1}{2}\left(1-u_{n}^{2}\right) \) y de término inicial \( u_{0}=0 \). P-2.1 Pruebe que para cualquier \( n \in \mathbb{N} \) se tiene \( u_{n} \in[0,1] \)0 answers -
both please !
Solve \( y^{\prime}+y=f(t) \), if \( y(0)=0 \), where \[ f(t)=\left\{\begin{array}{ll} 1 & 0 \leq t2 answers -
Q1. Solve \[ (x+2) \frac{d y}{d x}+y=f(x), \text { where } f(x)=\left\{\begin{array}{ll} 2 x, & 0 \leq x \leq 2, \\ 4, & x>2 . \end{array}\right. \]2 answers -
Consider the sequence defined recursively by xn+1 = Sqrt(xn +1), for any n ≥ 0. Q-4.1 Study the monotonicity of this sequence when x0 = 0. P-4.2 Show that if x0 = 0 then for any n ≥ 0 we have xn
Considere la sucesión definida recursivamente por \( x_{n+1}=\sqrt{x_{n}+1} \), para cualquier \( n \geq 0 \). P-4.1 Estudie la monotonicidad de esta sucesión cuando \( x_{0}=0 \). P-4.2 Demuestre q2 answers -
Consider the function f(x) = (1−x/1+x) P-6.1 Determine the fixed points of this function. P-6.2 Study the convergence of the method of successive approximations starting from x0 = 1. That is, study
Considere la función \( f(x)=\frac{1-x}{1+x} \). P-6.1 Determine los puntos fijos de esta función. P-6.2 Estudie la convergencia del método de las aproximaciones sucesivas partiendo de \( x_{0}=1 \2 answers -
2 answers
-
Consider the function 10.1 Determine the set of initial values for witch the newton iteration is defined 10.2 Show that for all the values found in the previous part, Newtons method converges 10.3 D
Considere la función \( f(x)=\sqrt[4]{(x-1)^{5}} \) P-10.1 Determine el conjunto de valores iniciales para los cuales la iteración de Newton está definida. P-10.2 Muestre que para todos los valores2 answers -
Let a>0 we want to approximate a ^-1 using only addition/subtraction and multiplication. For this we consider we consider Newtons method applied to the equation f(x) =0 where f(x):= 1/x-a 11.1 Wri
P-10.2 Muestre que para todos los valores encontrados en el inciso anterior, el método de Newton converge. P-10.3 Determine el orden de convergencia del método. Ejercicio 11. Sea \( a>0 \), se desea2 answers -
2 answers
-
1. Compute \( \iiint_{E}\left(x^{2}+y^{2}+z^{2}\right)^{1 / 2} d V \), where \( E=\left\{(x, y, z) \mid x \leqslant 0, y \leq 0, z \geqslant 0,4 \leq x^{2}+y^{2}+z^{2} \leq 16\right\} \).2 answers -
Solve the given initial-value problem. \[ y^{\prime \prime}+y^{\prime}+2 y=0, \quad y(0)=y^{\prime}(0)=0 \] \[ y(x)= \]2 answers -
\( h(x, y)=x^{2}+2 x y \) when \( -\sqrt{5 / 2} \leq x \leq \sqrt{5 / 2} \) \( x^{2}-2 \leq y \leq 3-x^{2} \) Find the absolute extreme values of \( h(x, y)=x^{2}+2 x y \) when \[ \begin{array}{l} -\2 answers -
show... if they are real numbers.
9. Demuestre que \( \mathrm{W}=\{(\mathrm{x}, \mathrm{y}, 2 \mathrm{x}-3 \mathrm{y}) / \mathrm{x} \), y son números reales \( \} \) es un subespacio del \( \mathrm{EV} \mathbb{R}^{3} \)2 answers -
determine … if they are integers
10. Determine si \( W=\left\{(x, y, z) / x, y\right. \), z son números enteros, es un subespacio del \( E V \mathbb{R}^{3} \)2 answers -
find the following laplace transform or inverse laplace transform find the following laplace transform or inverse laplace transform
Parte 1: Encuentre las siguientes transformadas de Laplace o transformada inversa de Laplace. (10 puntos cada uno) 1) \( L\left\{t^{3} e^{-t}\right\} \) 2) Hallar la transformada de Laplace de \( f(t)2 answers -
2 answers
-
2 answers
-
2 answers
-
2 answers
-
Find all the second order partial derivatives for the following: 1. \( f(x, y)=x+y+x y \) 2. \( f(x, y)=\sin x y \) 3. \( g(x, y)=x^{2} y+\cos y+y \sin x \)2 answers