Calculus Archive: Questions from October 20, 2023
-
1. Find \( \partial f / \partial x \) and \( \partial f / \partial y \) for (a) \( f(x, y)=e^{x y} \) (b) \( f(x, y)=x \cos x \cos y \) (c) \( f(x, y)=\left(x^{2}+y^{2}\right) \ln \left(x^{2}+y^{2}\ri1 answer -
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1. Dada \( y^{\prime}=x-3 y \) donde \( y(1)=0 \) a) Calcula \( y(1.4) \), por método de Euler con \( \mathrm{h}=0,1 \) b) Si la solución analítica de este problema es \[ y=\frac{3 x-2 e^{3-3 x}-1}1 answer -
11.(15 pts) Evaluate lim x 0 + tan sin H X + (tan 2x)*
11.(15 pts) Evaluate \[ \lim _{x \rightarrow 0+}\left(\frac{x^{3} \tan ^{-1}\left(\frac{1}{x}\right)}{\sin ^{-1} x}+(\tan 2 x)^{x}\right) . \]1 answer -
\[ y=3 x^{5}-5 x^{3}+6 \] relative maxima relative minima \[ \left.\begin{array}{l} (x, y)=\left(\begin{array}{l} x \\ (x, y) \end{array}\right) \\ x \end{array}\right) \] horizontal points of inflect1 answer -
Given \( f(x, y, z)=\sqrt{5 x-5 y+3 z} \), fi \( f_{x}(x, y, z)= \) \( f_{y}(x, y, z)= \) \( f_{z}(x, y, z)=\mid \)1 answer -
1 answer
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
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
-
2. (5 pts) Find f'(2, -1) if f : R² → R², f(x, y) = (x³, −5xy²). thank you
2. \( (5 \mathrm{pts}) \) Find \( f^{\prime}(2,-1) \) if \( f: \mathbf{R}^{2} \rightarrow \mathbf{R}^{2}, f(x, y)=\left(x^{3},-5 x y^{2}\right) \).1 answer -
Find \( \frac{d y}{d x} \) by implicit differentiation. \[ \begin{array}{l} x^{6}+x^{3} y^{3}+y^{9}=8 \\ \frac{d y}{d x}= \end{array} \]1 answer -
can you do number 20
Computing (1st-Order) Partial Derivatives In Exercises 1-78, compute the partial derivatives (i.e. 1st-order partials) of the given functions. 1. \( f(x, y)=x^{3} y^{4}+6 x^{5}-3 y^{3} \) 2. \( f(x, y1 answer -
can you do number 30
Computing (1st-Order) Partial Derivatives In Exercises 1-78, compute the partial derivatives (i.e. 1st-order partials) of the given functions. 1. \( f(x, y)=x^{3} y^{4}+6 x^{5}-3 y^{3} \) 2. \( f(x, y1 answer -
ecuaciones diferenciales de bernoulli, exactas
a. \( x^{2}=c y+y^{2} \) (ED Ortogonai) b. \( x^{2} p^{2}+x y p-6 y^{2}=0 \) c. \( p^{4}-(x+2 y+1) p^{2}+(x+2 y+2 x y) p^{2}-2 x y p=0 \) d. \( 16 x^{2}+2 p^{3}-p^{3} x=0 \) c. \( p^{3}-2 x y p+4 y^{20 answers -
Find the first partial derivatives of the function. \[ f(x, y, z)=x^{3} y z^{2}+9 y z \] \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]1 answer -
Find the first partial derivatives of the function. \[ \begin{array}{l} h(x, y, z, t)=x^{8} y \cos \left(\frac{z}{t}\right) \\ h_{x}(x, y, z, t)= \\ h_{y}(x, y, z, t)= \\ h_{z}(x, y, z, t)= \\ h_{t}(x1 answer -
1 answer
-
Evalute lim (x, y) → (0, 0) x4 + y4
\( \lim _{(x, y) \rightarrow(0,0)} \frac{x \cdot y^{4}}{x^{4}+y^{4}} \)1 answer -
1 answer
-
Evaluate \( \iiint_{\mathcal{W}} f(x, y, z) d V \) for the function \( f \) and region \( \mathcal{W} \) specified. \[ \begin{array}{l} f(x, y, z)=30 z \\ \mathcal{W}: x^{2} \leq y \leq 9,0 \leq x \le1 answer -
K- Verify the identity. sin 4 t - cos4 t = 1-2 cos² t Which of the following four statements establishes the identity? O A. sin4 t - cos4 t= (sin ² t - cos² t) (sin ² t - cos² t) = 1-2 cos² t 2
Verify the identity. \[ \sin ^{4} t-\cos ^{4} t=1-2 \cos ^{2} t \] Which of the following four statements establishes the identity? A. \( \sin ^{4} t-\cos ^{4} t=\left(\sin ^{2} t-\cos ^{2} t\right)\l1 answer -
1. Resuelva las E.D. con valores de frontera según corresponda: a) (20 pts) Variables Separables \[ \left(\frac{1}{4(y-2)}-\frac{1}{4(y+2)}\right) y^{\prime}=1 ; \quad y(0)=3 \]1 answer -
Resuelva la E.D. con valores de frontera
b) \( (20 \mathrm{pts}) \) Lineal \[ x y^{\prime}+y=\mathrm{e}^{x} ; \quad y(1)=3 . \]1 answer -
Resuelva la E.D. con valores de frontera
c) \( (20 \mathrm{pts})(\mathrm{No}) \) Exacta \[ x+\left(x^{2} y+4 y\right) y^{\prime}=0 ; \quad y(4)=0 \]1 answer -
c) Cuando un pastel se retira del horno, tiene una temperatura de \( 300^{\circ} \mathrm{F} \). Tres minutos más tarde, su temperatura es de \( 200^{\circ} \mathrm{F} \). ¿Cuánto tiempo le llevará1 answer -
21 COS X sin² x + 2 sin a dr table look up integrals
21. \( \int \frac{\cos x}{\sin ^{2} x+2 \sin x} d x \)1 answer -
Problema...: Se desea construir un pequeño centro comercial cuyo plano está dibujado más adelante. El centro comercial debe consistir de ocho tiendas rectangulares iguales( identificadas con una \(1 answer -
Given \( x \sqrt{y-z}-z e^{-x y}+y \cdot \arctan x=1 \), determine \( \frac{\partial z}{\partial x} \).1 answer -
SCALCET9 3.4.054. Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=(5+\sqrt{x})^{3} \] \[ \begin{array}{l} y^{\prime}= \\ y^{\prime \prime}= \end{array} \]2 answers -
1 answer
-
6. Differentiate each function a. y =(√x + ²)² b. F(y) = (-) (y + 5y³) y4, c. y = cos sin (tan лx) d. f(s) = e. y = s²+1 s² +4 COS TTX sin лx+cos TX
6. Differentiate each function ( 5 marks each -25 marks total) a. \( y=\left(\sqrt{x}+\frac{1}{\sqrt[3]{x}}\right)^{2} \) b. \( F(y)=\left(\frac{1}{y^{2}}-\frac{3}{y^{4}}\right)\left(y+5 y^{3}\right)1 answer -
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
\( \begin{array}{l}\int_{C} \mathbf{F} \cdot d \mathbf{r} . \\ \quad \begin{array}{l}\mathbf{F}(x, y)=x \mathbf{i}+y \mathbf{j} \\ C: \mathbf{r}(t)=(5 t+6) \mathbf{i}+t \mathbf{j}, \quad 0 \leq t \leq1 answer -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \[ z=0, x=0, z=y-x \text { and } y=2 . \] 1. \( \int_0 answers -
For each of the following, evaluate \( \frac{\partial f}{\partial y} \) at the point a. Justify. (a) \( f(x, y)=y \sin (x y)+x e^{-y^{2}}, \quad \mathbf{a}=\left(\frac{\pi}{6}, 2\right) \) (b) \( f(x,2 answers -
Let \( f(x, y)=\left\{\begin{array}{ll}x y\left(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}\right) & \text { if }(x, y) \neq(0,0) \\ 0 & \text { if }(x, y)=(0,0)\end{array}\right. \) (a) Find \( f_{x}(x, y) \) an1 answer -
1 answer
-
0 answers
-
1 answer
-
\( \begin{array}{l}D=\left\{(x, y) \mid(x-2)^{2}+y^{2} \leq 4\right\} \\ \text { ATE: } \int_{D} x d x d y\end{array} \)1 answer -
b) Solve the given initial value problem. \[ \begin{array}{ll} y^{\prime \prime}-64 y=16, & y^{\prime \prime}+y=8 \cos 2 x-4 \sin x \\ y(0)=1, y^{\prime}(0)=0 & y\left(\frac{\pi}{2}\right)=-1, y^{\pri1 answer -
0 answers
-
(1) Find the derivative of the following functions: dy dx (a) y = (8-5x)-³ (b) y = сsc(x²) r (c) y = ²² In
(1) Find the derivative \( \frac{d y}{d x} \) of the following functions: (a) \( y=(8-5 x)^{-3} \) (b) \( y=\sqrt[4]{\csc \left(\pi x^{2}\right)} \) (c) \( y=e^{x^{2} \ln x} \)1 answer -
1 answer
-
Find \( y^{\prime} \) and \( y^{\prime \prime} \) by implicit differentiation. \[ 2 x^{3}-5 y^{3}=8 \] \[ y^{\prime}=\frac{2 x^{2}}{5 y^{2}} \]1 answer -
Encuentre el número x en que f es discontinua, y determine si f es continua de la derecha, o de la izquierda, o ninguna de estas. f(x)={[2+x^(2)," si "x <= 0],[3-x," si "0 < x <= 3],[(x-3)^(
Encuentre el número \( x \) en que \( f \) es discontinua, y determine si \( f \) es continua de la derecha, o de la izquierda, o ninguna de estas. \[ f(x)=\left\{\begin{array}{ll} 2+x^{2} & \text {1 answer -
Resuelva las siguientes integrales propuestas en clase, aplicando el método correcto. Para realizar su trabajo puede consultar la diapositiva de la unidad 3 y sus apuntes de clase. 1. \( \int \operat1 answer -
1 answer
-
Find \( y \) as a function of \( x \) if \[ \begin{array}{l} \quad y^{\prime \prime \prime}-6 y^{\prime \prime}-y^{\prime}+6 y=0, \\ y(0)=-9, \quad y^{\prime}(0)=8, y^{\prime \prime}(0)=-79 . \\ y(x)=1 answer -
1 answer
-
1 answer
-
(2x^2+3у²—7)x - (3x^2+2y²-8) yy' = 0 Solve differential equations
\( \left(2 x^{2}+3 y^{2}-7\right) x-\left(3 x^{2}+2 y^{2}-8\right) y y^{\prime}=0 \)1 answer -
1 answer