Advanced Math Archive: Questions from January 15, 2023
-
evaluate the douple integral over the given region R
18. \( \iint_{R} x y e^{x y^{2}} d A, \quad R: \quad 0 \leq x \leq 2, \quad 0 \leq y \leq 1 \) 19. \( \iint_{R} \frac{x y^{3}}{x^{2}+1} d A, \quad R: \quad 0 \leq x \leq 1, \quad 0 \leq y \leq 2 \) 202 answers -
\[ \begin{array}{l} s^{4}+s^{3}+6 s^{2}+4 s+7=\left(s^{2}+\right. \\ \left(s^{2}+5\right)-s \end{array} \] Note: all edit boxes contain integers.2 answers -
Determine if the following vectors form a basis in R^3: 1. {(1, 5, 3), (2, 3, 4), (1, 9, 1)} 2. {(0, 2, 6), (1, 2, 3), (3, 4, 8)} Demonstrate the complete procedure as shown in the lessons. Also in
Ejercicios de Práctica: Determine si los siguientes vectores forman una base en \( \mathrm{R}^{3} \) : 1. \( \{(1,5,3),(2,3,4),(1,9,1)\} \) 2. \( \{(0,2,6),(1,2,3),(3,4,8)\} \) Demuestre el procedimi2 answers -
2 answers
-
2 answers
-
2 answers
-
Solve the following initial value problems a) \( x^{\prime}=-y \) \[ y^{\prime}=x \quad x(0)=1 \quad y(0)=1 \] b) \( \quad x^{\prime}=y \) \[ y^{\prime}=-x \quad x(0)=1 \quad y(0)=1 \]2 answers -
Calculate all derivatives. 1. \( f(z)=(2 c+\gamma) / 4 b . \quad d f / d z= \) ? 2. \( w(u)=6 u . \quad d w / d u= \) ? 3. \( f(k)=k^{2}+2 k . \quad d f / d k= \) ? 4. \( g(v)=1 / k, \quad d g / d k=2 answers