Calculus Archive: Questions from September 16, 2023
-
Which of the equations below are solutions to the PDE below? \[ \begin{array}{l} \frac{\partial^{2} u}{\partial x^{2}}+25 \pi^{2} u(x, y)=0 \\ u(x, y)=\left(y^{2}+3 y\right) \cos (5 \pi x)+y \sin (5 \1 answer -
1 answer
-
1 answer
-
1. Aplique los procesos estudiados para resolver problemas de valor inicial para obtener la solución particular de acuerdo a las condiciones dadas por el ejercicio. a) Determine \( f(x) \) para \( f^1 answer -
(4) Test for continuity at the point \( (0,0) \) : (a) \( f(x, y)=\left\{\begin{array}{l}\frac{2 x^{4}+y^{4}}{x^{2}+y^{2}},(x, y) \neq(0,0) \\ 0,(x, y)=(0,0)\end{array}\right. \) (b) \( f(x, y)=\left\1 answer -
Determine y' from 1. 2. e 3. y = 3219-4, >= 10log(x² +9) x ²³log(xy) + y = 2
Determine y' from 1. \( y=3^{2 x^{4}-4 x} \) 2. \( y={ }^{10} \log \left(x^{2}+9\right) \) 3. \( x^{3} \log (x y)+y=2 \) Determine y' from 1. \( y=3^{2 x^{4}-4 x} \) 2. \( y={ }^{10} \log \left(x^{2}1 answer -
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
Determine \( h=h(x, y) \) so that \[ \frac{\partial f}{\partial x}=\frac{h(x, y)}{\left(4 x^{2}+2 y^{2}\right)^{2}} \] when \[ f(x, y)=\frac{2 x^{2} y}{4 x^{2}+2 y^{2}} . \] 1. \( h(x, y)=4 x^{3} y \)1 answer -
1 answer
-
1 answer
-
Match the following differerential equations/IVP with the corresponding general solution/solution \[ \begin{array}{l} y^{\prime}=\frac{x^{2}}{y} \\ y^{\prime}=\frac{x^{2}}{y}, y(0)=-2 \\ y^{\prime}+y^1 answer -
Differentiate the function. \[ \begin{array}{c} y=\tan (\ln (a x+b)) \\ y^{\prime}=\frac{\sec ^{2}(\ln (a x+b))(a+b)}{a x+b} . \end{array} \]1 answer -
Given f(x, y) = y ln(6x - 5y), find fz(x, y) = fy(x, y) =
Given \( f(x, y)=y \ln (6 x-5 y) \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]1 answer -
1 answer
-
1 answer
-
Find \( \sin \theta \) and \( \tan \theta \) if \( \cos \theta=\frac{13}{85} \), assuming that \( 0 \leq \theta1 answer -
\( L_{1}(t)=(2-2 t, 0,2 t) \) con \( t \in \mathbb{R} \) y \( L_{2}(s)=(2-2 s, 2 s, 0) \) con \( s \in \mathbb{R} \). Adicionalmente, proporciona una ecuación \( A x+B y+C z+D=0 \) del plano \( \math1 answer -
please solve C and F
Find all the first and second order partial derivatives of \( f(x, y)=6 \sin (2 x+y)+8 \cos (x-y) \). A. \( \frac{\partial f}{\partial x}=f_{x}= \) B. \( \frac{\partial f}{\partial y}=f_{y}= \) C. \(1 answer