Calculus Archive: Questions from March 26, 2023
-
2 answers
-
Find the indefine integmal \( \int \cos ^{3} 6 \sin ^{2} 6 x d x \) A) \( \frac{\sin 6 x}{90}\left(5 \sin ^{2} 6 x-3 \sin ^{4} 6 x\right)+C \) B) \( \frac{\sin ^{6} x}{30}\left(5 \sin ^{2} 6 x-3 \sin2 answers -
Reverse the order of integration \[ \int_{0}^{1}\left(\int_{-\sqrt{2 y-y^{2}}}^{0} f(x, y) d x\right) d y+\int_{1}^{2}\left(\int_{y-2}^{0} f(x, y) d x\right) d y \]2 answers -
Suppose \( f^{\prime}(x)=\sin \left(3 x^{2}\right) \). \[ \begin{array}{l} \frac{d}{d x} f(8 x)= \\ \frac{d}{d x} f\left(6 x^{3}\right)= \end{array} \]2 answers -
2 answers
-
2 answers
-
Solve the differentiable equation: \( d y / d x=(y+x y) /(y+2) \) \[ \begin{array}{l} y+2 \ln |y|=x+(1 / 2) x^{2}+C \\ y+2 \ln |y|=x-(1 / 2) x^{2}+C \end{array} \] None of these. \[ y+\ln |y|=x+(1 / 22 answers -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-13 y^{\prime \prime}+40 y^{\prime}=84 e^{x} \] \[ y(0)=14, \quad y^{\prime}(0)=10, \quad y^{\prime \prime}(0)=13 \] \( y(2 answers -
2 answers
-
Find all the first and second order partial derivatives of \( f(x, y)=8 \sin (2 x+y)+4 \cos (x-y) \). A. \( \frac{\partial f}{\partial x}=f_{x}(x, y)= \) B. \( \frac{\partial f}{\partial y}=f_{y}(x, y2 answers -
Evaluate the following surface integrals \( \iint_{S}(\nabla \times \mathbf{F}) \cdot d \mathbf{S} \). 1. \( \mathbf{F}(x, y, z)=y \mathbf{i}-x \mathbf{j}+z x^{3} y^{2} \mathbf{k} \) and \( S=\left\{(0 answers -
Nombre: Karol Omar Duran Porras Encuentre el valor de " x " (10 puntos ) Alfa =(7x+20) Beta =(3x-25)0 answers
-
2 answers
-
2 answers
-
2. Sea r(x)= (sqrt (2-x), e^x - 1, ln (x+1))
2. Sea \( \mathbf{r}(x)=\left(\sqrt{2-x}, e^{x}-1, \ln (x+1)\right) \) a. Halle el dominio de \( \mathbf{r} \) b. Halle \( \lim _{x \rightarrow 0} \mathbf{r}(x) \) c. Halle \( \lim _{x \rightarrow 1}2 answers -
Consider the function. \[ f(x, y)=y+x e^{y} \] (a) Find \( \int_{0}^{2} f(x, y) d x \). \( 2 y+2 e^{y} \) (b) Find \( \int_{0}^{1} f(x, y) d y \). \( \frac{1}{2}+x[e-1]+C \)0 answers -
Calculate the double integral. \[ \iint_{R} \frac{3 x y^{2}}{x^{2}+1} d A, \quad R=\{(x, y) \mid 0 \leq x \leq 1,-2 \leq y \leq 2\} \]2 answers -
2 answers
-
1. Find the partial derivatives of: a. \( f(x, y)=y^{3}-4 x^{2} y-x \) b. \( g(x, y)=e^{2 y} \sin (x y) \) c. \( h(x, y, z) \sin (2 x+y+42) \)2 answers -
2. Para cada ecuación diferencial, dibuje el campo direcional. y dibuje la curva que pasa por el punto dado. (a) \( \left(10\right. \) points) \( y^{\prime}=y-2 x ; \quad(1,0) \) (b) \( \left(10\righ2 answers -
3. (10 points) Use el método de Euler con \( h=0.1 \) para aproximar el valor \( y(0.5) \) de la solución del problema de valor inicial \[ \frac{d y}{d x}=y+x y ; \quad y(0)=1 . \] Sugerencia: \( y(2 answers -
4. Resuelva las siguientes ecuaciones diferenciales separables. (a) \( \left(10\right. \) points) \( \left(y^{2}+x y^{2}\right) y^{\prime}=1 \) (b) \( (10 \) points \( ) \frac{d P}{d t}=\sqrt{P t} ; \2 answers -
2 answers
-
2 answers
-
(a) If \( y=\ln (x) \cdot x^{6} \), then \( y^{\prime}= \) (b) If \( H(x)=\sin \left(8^{x}\right) \), then \( \frac{d H}{d x}= \) (c) If \( f(x)=\frac{e^{3 x}}{x^{0.4}} \), then \( f^{\prime}(x)= \) (2 answers -
Find both first partial derivatives. \[ h(x, y)=e^{-\left(x^{9}+y^{9}\right)} \] \[ h_{x}(x, y)= \] \[ h_{y}(x, y)= \]2 answers -
If \( \left.l_{n}\right|^{1 / n} \rightarrow r>0 \), then \( \left|a_{n} x^{n}\right|^{1 / n} \rightarrow|x| r2 answers -
Use the Chain Rule to find \( \partial z / \partial s \) and \( \partial z / \partial t \). \[ \begin{array}{ll} \quad z=\arcsin (x-y), \quad x=s^{2}+t^{2}, \quad y=1-8 s t \\ \frac{\partial z}{\parti2 answers -
Esta actividad tiene como propósito de ayudar al estudiante a resolver integrales mediante sustituciones tngonométricas y evaluar integrale mediante la descomposición de funciones racionales en fac2 answers -
Use the simplex method. Minimize \( g=11 x+9 y+12 z \) subject to \[ \begin{aligned} x+y+z & \geq 6 \\ y+2 z & \geq 8 \\ x & \geq 2 . \end{aligned} \] \[ \begin{aligned} (x, y, z) & =( \\ g & = \end{a2 answers -
2 answers
-
Consider the region \( R \) in the first quadrant that is bounded by \( y=2-x^{2}, y=0 \), and \( y=x \). If for any function \( f(x, y) \) we have \( \iint_{R} f(x, y) d A=\int_{0}^{1} \int_{g_{1}(y)2 answers -
tch each function with one of the graphs below. 1. \( f(x, y)=e^{-y} \) 2. \( f(x, y)=\sqrt{4-4 x^{2}-y^{2}} \) 3. \( f(x, y)=\sqrt{4 x^{2}+y^{2}} \) 4. \( f(x, y)=1+y \)2 answers -
2 answers
-
0 answers
-
2 answers
-
\( \int \frac{\left(3 \tan ^{2} x+\tan x+4\right)\left(\tan ^{2} x+1\right)}{(\tan x-1)\left(\tan ^{2} x+2 \tan x+5\right)} d x \)0 answers -
2 answers
-
2 answers
-
2 answers
-
Find the value of the double integral \[ I=\iint_{A}(4 x-y) d x d y \] hen \( A \) is the region \[ \{(x, y): y \leq x \leq \sqrt{y}, \quad 0 \leq y \leq 1\} \]2 answers -
2 answers
-
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=e^{3 e^{x}} \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]2 answers -
2 answers
-
2 answers
-
3 answers
-
0 answers
-
2 answers
-
2 answers
-
Find all possible functions with the given derivative. 1. If \( y^{\prime}=\sin (3 t) \), then \( y= \) 2. If \( y^{\prime}=\cos \left(\frac{t}{3}\right) \), then \( y= \) 3. If \( y^{\prime}=\sin (32 answers -
2 answers