Calculus Archive: Questions from June 04, 2023
-
Solve the following differential equations:
\( \left(2 x+\sin y-y e^{-2 x}\right) d x+\left(x \cos y+\cos y+e^{-2 x}\right) d y=0 \) \( \left(x \cos x+\frac{y^{2}}{x}\right) d x=\left(x \frac{\sin x}{y}+y\right) d y \)2 answers -
Find dy/dx if y = 2(5x^2 − 4)^3
\( \frac{d y}{d x} \) if \( y=2\left(5 x^{2}-4\right)^{3} \) \[ \frac{d y}{d x}=6\left(5 x^{2}-4\right)^{2} \] \[ \frac{d y}{d x}=6(10 x)^{2} \] \[ \frac{d y}{d x}=6\left(5 x^{2}-4\right)^{2}(10 x) \]2 answers -
2 answers
-
0 answers
-
2 answers
-
0 answers
-
2 answers
-
2 answers
-
2 answers
-
0 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
0 answers
-
2 answers
-
1 answer
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
0 answers
-
2 answers
-
2 answers
-
0 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
0 answers
-
0 answers
-
2 answers
-
0 answers
-
0 answers
-
2 answers
-
2 answers
-
2 answers
-
2 answers
-
0 answers
-
0 answers
-
2 answers
-
2 answers
-
2 answers
-
0 answers
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
Evaluate the integral. Z 4 0 Z √ 16−x 2 − √ 16−x 2 Z √ 16−x 2−z 2 − √ 16−x 2−z 2 1 (x 2 +y 2 +z 2) 1/2 dy dz dx =
Evaluate the integral. \[ \int_{0}^{4} \int_{-\sqrt{16-x^{2}}}^{\sqrt{16-x^{2}}} \int_{-\sqrt{16-x^{2}-z^{2}}}^{\sqrt{16-x^{2}-z^{2}}} \frac{1}{\left(x^{2}+y^{2}+z^{2}\right)^{1 / 2}} d y d z d x= \]2 answers -
1 answer
-
1 answer
-
1 answer
-
1 answer
-
Differentiate the given function. \[ \begin{array}{l} y=-\frac{9}{x^{1.1}}+\frac{2}{x^{-2.3}} \\ y^{\prime}=-\frac{9}{1.1 x^{0.1}}-\frac{2}{2.3 x^{-3.3}} \\ y^{\prime}=\frac{9.9}{x^{2.1}}+6.6 x^{3.3}2 answers -
Evaluate \( \iiint_{\mathcal{W}} f(x, y, z) d V \) for the function \( f \) and region \( \mathcal{W} \) specified: \[ f(x, y, z)=48(x+y) \quad \mathcal{W}: y \leq z \leq x, 0 \leq y \leq x, 0 \leq x2 answers -
5. 18Mmint Find and describe the domain of \( f(x, y, z)=\sqrt{x}+\sqrt{y}+\sqrt{z}+\ln \left(4-x^{2}-y^{2}-z^{2}\right) \). main of \( f(x, y, z)=\left\{(x, y, z) \in R^{3} \mid\right. \)2 answers -
2 answers
-
Evalúe la integral. (Recuerde usar valores absolutos cuando proceda. Utilice \( C \) como \[ \int \frac{9 x d x}{x^{4}-a^{4}} \]2 answers -
Evalúe la integral. (Recuerde usar valores absolutos cuando proceda. Utilice \( C \) como la constante de integración.) \[ \frac{\int \frac{5 x d x}{x^{4}-a^{16}}}{\frac{5 x^{-2}}{-2}-\frac{a^{-16}}2 answers -
Evalúe la integral indefinida. (Utilice \( C \) como la constante de integración. \[ \int \frac{a+b x^{7}}{\sqrt{8 a x+b x^{8}}} d x \] \[ 2 \sqrt{8 a^{2} x+a b x^{8}}+2 \sqrt{8 b x^{2} a+b^{2} x^{12 answers -
Find an implicit solution of the initial value problem \[ \left\{\begin{aligned} \left(6 x^{2} y^{2}+4 e^{x}-2 y \sin (2 x)\right)+\left(4 x^{3} y+\cos (2 x)\right) \frac{d y}{d x} & =0 \\ y(0) & =1 \2 answers -
2 answers
-
resolver la ecuación diferencial Parcial Lineal
Resolver EDPL \[ \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}=x \]0 answers -
Divide. \[ \frac{25 x^{2}-16}{25 x^{2}+40 x+16} \div(30 x-24) \] \[ \frac{25 x^{2}-16}{25 x^{2}+40 x+16} \div(30 x-24)= \]2 answers -
Find the limit
\( \lim _{P \rightarrow(\pi, \pi, 0)}\left(\sin ^{2} x+\cos ^{2} y+\sec ^{2} z\right) \)2 answers -
Differentiate. \[ \begin{array}{c} y=\frac{\sqrt{x}}{6+x} \\ y^{\prime}=\frac{6-x}{2 \sqrt{x}(6+x)^{2}} \end{array} \]2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{c} y=\frac{\ln (4 x)}{x^{6}} \\ y^{\prime}=\frac{1-\ln \left(4096 x^{6}\right)}{x^{7}} \\ y^{\prime \prime}=\frac{-13+\ln \left(19342 answers -
2 answers
-
For the function, find the partials \( f_{\chi}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=4 x^{4}-7 x^{3} y^{2}-6 x y+7 \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers -
For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=4 x^{2} e^{y} \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers -
For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=(x+y)^{-3} \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers