Calculus Archive: Questions from October 24, 2023
-
If \( f(x, y)=\frac{x^{2} y}{\left(5 x-y^{2}\right)} \), find the following. (a) \( f(1,4) \) (b) \( f(-5,-1) \) (c) \( f(x+h, y) \) (d) \( f(x, x) \)1 answer -
number 32
27-34 Calculate the double integral. 27. \( \iint_{R} x \sec ^{2} y d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 2,0 \leqslant y \leqslant \pi / 4\} \) 28. \( \iint_{R}\left(y+x y^{-2}\right) d1 answer -
94. ƒ(x, y, z) = 22 x + y
94. \( f(x, y, z)=\frac{2 z}{x+y} \) FINDING HIGHER-ORDER PARTIAL DERIVATIVES In Exercises 91, 92, 93, and 94, show that the mixed partial derivatives \( f_{x y y}, f_{y x y} \), and \( f_{y y x} \0 answers -
3. Resuelve el problema \[ \begin{array}{c} u_{t}=u_{x x}, \quad x>0 \quad t>0 \\ u_{x}(0, t)=u(0, t)=0 \\ u(x, 0)=u_{0} \end{array} \]0 answers -
Change the order of integration of \( \int_{0}^{6} \int_{0}^{4-2 x / 3} \int_{0}^{3-x / 2-3 y / 4} f(x, y, z) d z d y d x \) in \( d y d x d z \)1 answer -
Con procedimiento por favor, gracias.
Paree: 1. \( L^{-1}\left\{\begin{array}{c}e^{-35} \\ s^{5}\end{array}\right\} \) a) \( u(t-2) \cos 4(t-2) \) 2. \( L^{-1}\left\{\frac{e^{-2 s}}{s(s+1)}\right\} \) b) c) \( 4 \sinh 3(t-4) u(t-4) \) 3.0 answers -
help
3. Find the solution to the IVP \( \frac{d y}{d x}=(1-2 x) y^{2} \) and \( y(0)=-\frac{1}{6} \). (A) \( y=\frac{1}{x^{2}-x-6} \) (B) \( y=\frac{1}{x^{2}-x+6} \) (C) \( y=\frac{1}{x^{2}+x+6} \) (D) \(1 answer -
vi. \( \int_{1}^{2}\left(\frac{1}{x^{2}}-\frac{4}{x^{3}}\right) d x \) vii. \( \int x e^{-x^{2}} d x \) viii. \( \int \frac{x^{3}}{x^{4}-5} d x \) ix. \( \int \sin t \sqrt{1+\cos t} d t \) x. \( \int1 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
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
find dy/dx
(1) Find \( \frac{d y}{d x} \) a) \[ \begin{array}{l} y=\sin \left(x^{3}+e^{x}\right)\left(x+3 x^{4}\right) \\ \frac{d y}{d x}= \end{array} \] b) \( y=\frac{e^{-x}}{x \cos \sqrt{x}} \) Fo te expe \( x1 answer -
1. Solve the following differential equations (a) \( y^{\prime \prime}-9 y=0 \) (b) \( y^{\prime \prime}-9 y^{\prime}=0 \) (c) \( y^{\prime \prime}-4 y^{\prime}+9 y=0 \) (d) \( y^{\prime \prime}-4 y^{1 answer -
Simplify the following expression. cos2v (21-28 cos 2 v) ² + v) ² + sin ² v (21 - 28 sin ² v) ²
Simplify the following expression. \[ \cos ^{2} v\left(21-28 \cos ^{2} v\right)^{2}+\sin ^{2} v\left(21-28 \sin ^{2} v\right)^{2} \]1 answer -
0 answers
-
1 answer
-
Evaluate the double integral. y 11₁2²2² +1₁, dA, D = {(x, y) | 0 ≤ x ≤ 2,0 ≤ y ≤ √XI
Evaluate the double integral. \[ \iint_{D} \frac{y}{x^{2}+1} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq \sqrt{x} \]1 answer -
1 answer
-
3) Solve the IVP. \[ y^{\prime \prime}-4 y^{\prime}=6 e^{3 t}-3 e^{-t}, \quad y(0)=1, \quad y^{\prime}(0)=-1 \]1 answer -
Solve the IVP
3) Solve the IVP. \[ y^{\prime \prime}-4 y^{\prime}=6 e^{3 t}-3 e^{-t}, \quad y(0)=1, \quad y^{\prime}(0)=-1 \]1 answer -
5) Usando reducción de orden resuelva la siguiente EDO, dada la solución particular \( y_{1}=x \) \[ \left(1-x^{2}\right) y^{\prime \prime}+2 x y^{\prime}-2 y=0 ; y(0)=1, y^{\prime}(0)=0 \]1 answer -
INSTRUCTIONS Objetivo: Esta actividad tiene como propósito ayudar al estudiante a reconocer la función cuadrática dada en la forma \( f(x)=a x^{2}+b x+c \) para rescribirla en \( f(x)=a(x-h)^{2}+k1 answer -
2. Hallar una función \( f \) tal que \( \nabla f=e^{x} \cos (y) \mathbf{i}-e^{x} \sin (y) \mathbf{j}+z \mathbf{k} \)1 answer -
1 answer
-
Evaluate \( \iiint_{B}\left(4 z^{3}+3 y^{2}+2 x\right) d V \) \[ B=\{(x, y, z) \mid 0 \leq x \leq 7,0 \leq y \leq 7,0 \leq z \leq 7\} \]1 answer -
#3 #8 #9 #12
\( 3-16 \) = Find \( d y / d x \) by implicit differentiation. 3. \( x^{3}+y^{3}=1 \) 4. \( 2 x^{3}+x^{2} y-x y^{3}=2 \) 5. \( x^{2}+x y-y^{2}=4 \) 6. \( y^{5}+x^{2} y^{3}=1+x^{4} y \) 7. \( y \cos x=1 answer -
(2) If \( \vec{r}(t)=(a \cos t, a \sin t), t \in[0,2 \pi] \), and \( \vec{F}(x, y)=(-y, x) \). Evaluate \( \int_{C} \vec{F} \cdot d \vec{r} \).1 answer -
\( \begin{array}{l}x, y) d x \text { and } \int_{0}^{3} f(x, y) d y \\ f(x, y)=9 x+3 x^{2} y^{2}\end{array} \)1 answer -
Evaluate the double integral. \[ \iint_{D}(2 x+y) d A, \quad D=\{(x, y) \mid 1 \leq y \leq 5, y-4 \leq x \leq 4\} \]1 answer -
0 answers
-
Find y' (2) if y = cos(x) 1-cos(x)
\( y^{\prime}\left(\frac{\pi}{2}\right) \) if \( y=\frac{\cos (x)}{1-\cos (x)} \)1 answer -
1. Evaluate the integral fff (x + 3y + 2z) dV if: D = {(x, y, z) |0 ≤ x ≤ 2,0 ≤ y ≤ 3,0 ≤z≤ 1}
Evaluate the integral \( \iiint_{D}(x+3 y+2 z) d V \) if: \[ D=\{(x, y, z) \mid 0 \leq x \leq 2,0 \leq y \leq 3,0 \leq z \leq 1\} \]1 answer -
1 answer
-
#14
\( 3-16 \). Find \( d y / d x \) by implicit differentiation. 3. \( x^{3}+y^{3}=1 \) 4. \( 2 x^{3}+x^{2} y-x y^{3}=2 \) 5. \( x^{2}+x y-y^{2}=4 \) 6. \( y^{5}+x^{2} y^{3}=1+x^{4} y \) 7. \( y \cos x=x1 answer -
1. ¿Cuál de estas integrales representa el área de la superficie generada al girar la curva \( r=e^{2 \theta}, \quad 0 \leq \theta \leq \frac{\pi}{2} \), alrededor de la línea \( \theta=\frac{\pi}1 answer -
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
Find y' and y". y' = y" = y = x² In(9x) X
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=x^{2} \ln (9 x) \] \[ y^{\prime}= \]1 answer -
can you plz do question 32
Analyzing the Graph of a Function In Exercises 9-36, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to1 answer -
1 answer
-
1 answer
-
Calculate y'
(g) \( y=(\cos x)^{x} \) (h) \( y=10^{\tan (\pi \theta)} \) (i) \( y=\cos \left(e^{\sqrt{\tan 3 x}}\right) \)1 answer -
differentiate
(31) \( f(x)=e^{-x^{2} / 2} \rightarrow \) (33.) \( y=e \sqrt{x-7} \) 43.) \( y=x e^{-2 x}+e^{-x}+x^{3} \)1 answer -
1 answer
-
5. Suponga que la parábola \( y=a x^{2}+b x+c \) y la recta \( y=m x+n \) se intersecan en \( x=A \) y \( x=B \) con \( A1 answer -
Please show all your work. NO WORK - NO CREOIT Formula sheet \( \mathrm{c}^{2} \) Given \( f(x, y)=6 x^{8} \cos \left(y^{7}\right) \), find \( f_{x y}(x, y)= \)1 answer -
1 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 \( z=0, x=0, z=y-4 x \) and \( y=8 \). \[ \begin{arra1 answer -
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
2. \( y^{\prime} \) where \( y=7 \sqrt{x} e^{x} \) 3. \( \frac{d y}{d x} \) where \( y=x e^{x} \tan x \) 4. \( f^{\prime}(x) \) where \( f(x)=\frac{x-2}{4 x+5} \). 5. \( \frac{d f}{d x} \) where \( f(1 answer -
1 answer
-
Calculate the Hessian for the function f(x, y) = x³cos(y) — xsin(y). 1 point H = H = H H = 6cos(y) -3x²sin(y) - cos(y) [-2, 6xcos(y) -3x² sin(y) - cos(y) = [- 6cos(x) -3x² sin(y) — cos(y) -3x
Calculate the Hessian for the function \( f(x, y)=x^{3} \cos (y)-x \sin (y) \). 1 point \[ H=\left[\begin{array}{cc} 6 \cos (y) & -3 x^{2} \sin (y)-\cos \left(y^{2}\right) \\ -3 x^{2} \sin (y)-\cos (y1 answer