Calculus Archive: Questions from November 10, 2022
-
0 answers
-
0 answers
-
0 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
find the derivative
a) \( y=\frac{x+8 x^{2}}{x^{2}+x} \) b) \( y=\sqrt{x}-\frac{1}{\sqrt{x}} \) c) \( y=x^{2} \cdot \ln 3 x^{2} \) d) \( y=\frac{\left(x^{2}+8 x\right)^{3}}{x+5} \)2 answers -
The multivariable function \( f(x, y)=4 x^{2}+2 x y-7 y^{2}+13 x-6 y+4 \), Find: i. \( f(x, y) \) ii. \( f(x, y) \) iii. \( f(x, y) \)2 answers -
5. Halle el área de la región encerrada dentro del bluque grande y fuera del buqle pequeño de la curva: \( r=3+4 \sin (t) \).2 answers -
2 answers
-
2 answers
-
Find the Jacobian transformation. \[ \begin{array}{c} J(r, \theta, \phi)=\frac{\partial(x, y, z)}{\partial(r, \theta, \phi)} \\ x=r \cdot \sin (\theta) \quad, \quad y=r \cdot \cos (\theta), \quad z=r2 answers -
Solve the initial value problem
21. \( y^{\prime \prime}-2 y^{\prime}+y=0 ; y(0)=4, y^{\prime}(0)=0 \)2 answers -
Find the Jacobian transformation. \[ J(r, \theta, \phi)=\frac{\partial(x, y, z)}{\partial(r, \theta, \phi)} \] \( 10 \mathrm{pts} \) \[ x=r \cdot \sin (\theta) \quad, \quad y=r \cdot \cos (\theta), \q2 answers -
2 answers
-
2 answers
-
\( x=8 w-(8 u+6 v), y=4 v-6 u-4 w \), and \( z=5 u-v-5 w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)2 answers -
\( x=6 u v-u, y=8 u v w-4 u v \), and \( z=-6 u v w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)2 answers -
Evaluate the following integral. \[ \int e^{-3 \theta} \sin 9 \theta d \theta \] \[ \int e^{-3 \theta} \sin 9 \theta d \theta= \]2 answers -
2 answers
-
Find the first partial derivatives. See Example 1. \[ g(x, y)=9 e^{x / y} \] \[ g_{x}(x, y)= \] \[ g_{y}(x, y)= \]2 answers -
2 answers
-
Use the Fundamental Theorem of Calculus to find \( y^{\prime} \). \[ y=\int_{\pi / 6}^{\sqrt{x}} \theta \tan \theta d \theta \]2 answers -
Find the Jacobian of the transformation. \[ x=6 u^{4} v^{2}, y=u^{3} / v^{3} \] \( \frac{\partial(x, y)}{\partial(u, v)}=\frac{108 u^{6}}{v^{2}} \)2 answers -
Urgent help please
Find the gradient vector field \( \left(\vec{F}(x, y, z)\right. \) ) of \( f(x, y, z)=y \cos \left(\frac{2 z}{x}\right) \). \[ \vec{F}(x, y, z)= \]2 answers -
(1 point) Given the function \( f(x, y)=x^{2}+2 x y+3 y^{2}+4 x-(-2) y \). Find the first and second partial derivatives of the function. \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x 1}(x,1 answer -
2 answers
-
a)b)
\( \int_{4}^{5} \int_{1}^{3} x y e^{x+y} d y d x \) \( \int_{2}^{6} \int_{8}^{10}(x+\ln y) d y d x \)2 answers -
(2 points) Solve the initial value problem \[ y^{\prime \prime}+4 x y^{\prime}-16 y=0, y(0)=4, y^{\prime}(0)=0 \] \[ y= \]2 answers -
Analizar y dibujar la gráfica de \( f(x)=x^{4}+2 x^{3}-3 x^{2}-4 x+4 \) respondiendo los siguiente: n) Primera derivada o) Segunda derivada p) Intersecciones con el eje \( x \) q) Intersección con e2 answers -
may I get help with #6 please? Thank you so much!
1-8 Find (a) the curl and (b) the divergence of the vector field. 1. \( \mathbf{F}(x, y, z)=x y^{2} z^{2} \mathbf{i}+x^{2} y z^{2} \mathbf{j}+x^{2} y^{2} z \mathbf{k} \) 2. \( \mathbf{F}(x, y, z)=x^{32 answers -
(1 point) Given the function \( f(x, y)=10 x y-9 x^{2}+5 y^{2}+9 x-2 y \). Find the first and second partial derivatives of the function. \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x x}(x,2 answers -
2 answers
-
5. Determine whether the vector field \( \vec{F} \) is conservative. If so, find a function \( f \) such that \( \vec{F}=\vec{\nabla} f \) (a) \( \vec{F}(x, y)=\left(\frac{1}{x}+\cos y\right) \vec{\im2 answers