Calculus Archive: Questions from October 10, 2023
-
a.1: Solve any 2 of the following D.Es. 1. \( \left(e^{x} \sin 2 y-3 x\right) d x+\left(2 e^{x} \cos ^{3} y-2 y\right) d y=0 \). 2. \( y \frac{d y}{d x}=x e^{x-y} \), 3. \( \frac{d y}{d x}+\frac{1}{x}1 answer -
9. f(x, y) = y. (Recall: If f(z) = b², f'(z) = b² lnb) (a) f(x, y) = (b) fy(x, y) = (c) fxx(x, y) = (d) fay(x, y) = (e) fyx (x, y) = (f) fyy(x, y) =
9. \( f(x, y)=y^{x} \). (Recall: If \( f(z)=b^{z}, f^{\prime}(z)=b^{z} \ln b \) ) (a) \( f_{x}(x, y)= \) (b) \( f_{y}(x, y)= \) (c) \( f_{x x}(x, y)= \) (d) \( f_{x y}(x, y)= \) (e) \( f_{y x}(x, y)=1 answer -
1 answer
-
Find the Laplace transform by defining the following problems.
Hallar la transformada de Laplace por la definición los siguientes problemas: 1. \( f(t)=e^{t+7} \) 2. \( f(t)=\cos t \) 3. \( f(t)=t e^{4 t} \) 4. \( f(t)=\left\{\begin{array}{ll}t, 0 \leq t1 answer -
1 answer
-
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-12 y^{\prime \prime}+27 y^{\prime}=0 \] \[ \begin{array}{l} y(0)=4, \quad y^{\prime}(0)=7, \quad y^{\prime \prime}(0)=3 \2 answers -
1 answer
-
1. Definir el producto escalar de 2 vectores 2. Definir qué se entiende por vectores ortogonales. Si 2 vectores no son paralelos ni paralelos ni ortogonales, ¿Cómo se puede calcular el ángulo que1 answer -
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
0 answers
-
1 answer
-
1 answer
-
0 answers
-
0 answers
-
1 answer
-
Practice Find the derivative \( \left(y^{\prime}=\frac{d y}{d x}\right) \) 1. \( y=2 x^{3}+x^{2}-3 x-1 \) 2. \( y=2 e^{x}+e^{3}-\sqrt{x} \) 3. \( y=\frac{1}{x^{2}}+\frac{2}{e^{3 x}} \) 4. \( y=\frac{e1 answer -
Find the derivative 1. \( y=x^{2} \sin (x) \). 2. \( y=3 \sqrt{x} \ln (3 x) \). 3. \( y=x^{2} e^{-x} \). 4. \( y=x^{2} \cos (3 x)+3 \sin (4 x) \). 5. \( y=3 x e^{-x} \sec \left(\frac{x}{2}\right) \)1 answer -
Find the derivative 1. \( y=\frac{x^{2}}{\sin (x)} \). 2. \( y=\frac{3 x^{2}}{x^{2}+3 x-1} \). 3. \( y=\frac{t e^{2 t}}{2 \cos (t)} \). 4. \( y=\frac{\ln (2 x)}{e^{3 x}} \).1 answer -
Find the derivative 1. \( y=\left(x^{2}+3 x-1\right)^{3} \) 2. \( y=3 \cos \left(3 x^{3}+2 x-1\right)+2 e^{\tan (x)} \) 3. \( y=\sin ^{2}\left(2 x^{2}-1\right)+e^{x^{2}} \) 4. \( y=\ln \left(2 x^{3}-51 answer -
Given f(x, y) = cos(—4x – 6y), find fax(x, y) = 16 cos(4x + 6y) fry(x, y) = fyy(x, y) = Add Work Submit Question X
\( \begin{array}{l}\text { Given } f(x, y)=\cos (-4 x-6 y) \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y y}(x, y)=\end{array} \)1 answer -
1 answer
-
0 answers
-
como se resuelve? si se puede paso a paso mejor, necesito el tiempo
\( \int_{0}^{\mathrm{t}} \mathrm{dt}=\int_{0}^{2,000} \frac{\mathrm{dy}}{\sqrt{12 \mathrm{y}+0.02 \mathrm{y}^{2}}} \)1 answer -
Descripción de la actividad: debes resolver los siguientes ejercicios incluyendo su desarrollo completo. Ejercicio 1. Calcula los límites de las siguientes funciones: a) \( \lim _{x \rightarrow \inf1 answer -
Ejercicio 3. Calcula las siguientes derivadas: a) \( f(x)=\left(2 x^{2}-3 x+1\right)^{5} \) b) \( f(x)=\ln x \sqrt{x} \) c) \( f(x)=\frac{x^{2}+x-1}{\sqrt{x}} \) d) \( f(x)=\left[\ln \left(3 x^{2}+2 x1 answer -
Ejercicio 4. Dada la función \( y=a x^{3}-x^{2}+b x+c \), determina \( a, b \) y c sabiendo que la función pasa por el punto \( (0,5) \) y tiene extremos relativos en \( x=-1 \) y \( x=3 \).1 answer -
Ejercicio 5. En una circunferencia de radio 2 hay inscrito un rectángulo de lados \( x \) e \( y \). Calcula la longitud de esos lados para que el área del rectángulo sea máxima y calcula el valor1 answer -
Ejercicio 6. Estudia la gráfica de la siguiente función (dominio, simetría, puntos de corte, continuidad, asíntotas, crecimiento y extremostrelativos, concavidad y puntos de inflexión): \[ f(x)=\1 answer -
1. Clasficar si los siguientes pares de vectores son paralelos, perpendiculareso ninguno de los dos. a. \( \vec{A}=i+2 j-k \quad \vec{B}=2 i+2 j+6 k \) b. \( \overrightarrow{\mathrm{C}}=\mathrm{i}+2 \1 answer -
1 answer
-
7. \( \iiint_{B} y d V \), where \[ E=\{(x, y, z) \mid 0 \leqslant x \leqslant 3,0 \leqslant y \leqslant x, x-y \leqslant z \leqslant x+y\} \]1 answer -
Use implicit differentiation to find y' = In(x) y y = + In(y) ४ = 9 dy dx
Use implicit differentiation to find \( y^{\prime}=\frac{d y}{d x} \). \[ \frac{\ln (x)}{y}+\frac{\ln (y)}{x}=9 \] \[ y^{\prime}= \]1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-9 y^{\prime \prime}+20 y^{\prime}=0 \] \[ \begin{array}{l} y(0)=1 \quad v^{\prime}(\Pi)=8 \quad \vee^{\prime \prime}(\Pi)1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-6 y^{\prime \prime}-y^{\prime}+6 y=0, \] \( y(0)=3 . \quad v^{\prime}(0)=-3 . \quad v^{\prime \prime}(0)=-137 \) \( y(x)1 answer -
!! (c) f(x) = 2x x² (ex) x10x+15 · e¹+2x
(c) \( f(x)=\frac{x^{2 x}(e x)}{x^{10 x+15}} \cdot e^{1+2 x} \)0 answers -
12. a) Expresar \( \int_{0}^{1} \int_{0}^{x^{2}} x y d y d x \) como una integral sobre el triángulo \( D^{*} \), que es el conjunto de puntos \( (u, v) \) que cumplen \( 0 \leqslant u \leqslant 1,01 answer -
1 answer
-
57. Let \[ f(x, y)=\left\{\begin{array}{ll} 0 & \text { if } y \leqslant 0 \text { or } y \geqslant x^{4} \\ 1 & \text { if } 01 answer -
Find the domain of the function \[ f(x, y)=\ln \left(2-x^{2}-7 y^{2}\right) \text {. } \] 1. \( \left\{(x, y): \frac{1}{2} x^{2}+\frac{7}{2} y^{2}>1\right\} \) \( \begin{array}{l}\left\{(x, y): \frac1 answer -
5. Paree las funciones con sus gráficas, (a) \( y=\sec \left(2 x+\frac{\pi}{4}\right) \) (b) \( y=1-\tan \left(x-\frac{\pi}{3}\right) \) (c) \( y=1+\cot (2 x) \) (d) \( y=\tan \left(3 x-\frac{\pi}{2}1 answer -
Given the integral choose the best coordinate system. \[ \int_{0}^{5} \int_{0}^{\sqrt{25-x^{5}}} \int_{0}^{-2 x-2 y+100} f(x, y, z) d z d y d z \] \[ \int_{0}^{5} \int_{0}^{x^{2}+25} \int_{0}^{2 z+2 y1 answer -
1 answer
-
8. Find y' if y = ln (sin(cos x)) using three different methods.
8. Find \( y^{\prime} \) if \( y=\ln (\sin (\cos x)) \) using three different methods.1 answer -
\[ f(x)=\frac{\tan x-4}{\sec x} \] find \( f^{\prime}(x) \). Find \( f^{\prime}\left(\frac{\pi}{4}\right) \)1 answer -
Find y' and y". y' = y" = = y = In(sec(8x) + tan(8x)) Need Help? Submit Answer X Read It
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\ln (\sec (8 x)+\tan (8 x)) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]1 answer -
1 answer
-
1 answer
-
1 answer
-
I. Solve the initial value problems: 1. \( y^{\prime \prime}-6 y^{\prime}-7 y=0, \quad y(0)=1 \), and \( y^{\prime}(0)=2 \) 2. \( y^{\prime \prime}+4 y^{\prime}+5 y=0, \quad y(0)=2 \), and \( y^{\prim1 answer -
For the given parametric equations, find the points \( (x, y) \) corresponding to the parameter values \( t=-2,-1,0,1,2 \). \[ \begin{array}{ll} & x=3 t^{2}+3 t, \quad y=3^{t+1} \\ t=-2 & (x, y)=( \\1 answer -
17. \( \lim _{x \rightarrow 0}\left[\frac{x^{3}-2 x^{2}-8 x}{x^{3}-4 x}\right]=2 \). a. true b. false1 answer -
Calculate (6, 6, 3), where f(x, y, z) = xyz. (6,6,3)=
Calculate \( f_{z}(6,6,3) \), where \( f(x, y, z)=x y z \). \[ f_{2}(6,6,3)= \]1 answer -
2. Evalúe cada expresión sin utilizar calculadora. (a) \( \cos ^{-1}\left(\cos \left(\frac{7 \pi}{4}\right)\right) \) (b) \( \operatorname{sen}\left(\operatorname{sen}^{-1}\left(-\frac{3}{4}\right)\1 answer -
3. Use funciones trigonométricas en un círculo de radio apropiado para evaluar las siguientes expresiones. (a) \( \operatorname{sen}\left(\tan ^{-1}(4)\right) \) (b) \( \csc \left(\cos ^{-1}\left(-\1 answer -
Solve the differential equation. \[ \begin{array}{c} y^{\prime}=23 y^{2} \sin (x) \\ y=\frac{1}{23 \sin (x)+C} \end{array} \] \( y=2 \) \[ y=-\frac{1}{23 \sin (x)+C} \] \[ y=0 \] \[ y=\frac{1}{23 \cos1 answer -
Solve the differential equation. \[ \begin{array}{r} (6+\tan (y)) y^{\prime}=x^{2}+6 \\ 6 y-\ln (|\cos (y)|)+C= \end{array} \]1 answer -
If find f'(x). secx-tan x(tanx-2) secx Find f'(). sec²()-tan() (tan (5)-2) sec 江2 کے tanz 2 - f(x) = secz
If \[ f(x)=\frac{\tan x-2}{\sec x} \] find \( f^{\prime}(x) \). \[ \frac{\sec ^{2} x-\tan x(\tan x-2)}{\sec x} \] Find \( f^{\prime}\left(\frac{\pi}{2}\right) \). \[ \frac{\sec ^{2}\left(\frac{\pi}{2}1 answer -
1 answer
-
Given y = -3e cos(x). Find y' and y". y'= -5x y"= Question Help: Video Submit Question xo-3e* cos(x) + 3e* sin(x)
Given \( y=-3 e^{x} \cos (x) \) \[ \begin{array}{l} y^{\prime}= \\ y^{\prime \prime}= \end{array} \] Question Help: \( \square \) Video1 answer -
Calculate d²y / dx² y = e^-x + e^x
Calculate \( \frac{d^{2} y}{d x^{2}} \) \[ \frac{d^{2} y}{d x^{2}}= \]1 answer -
(1 point) if \[ f(x)=\frac{4 x^{2} \tan x}{\sec x} \] find \( f^{\prime}(x) \). Find \( f^{\prime}(3) \).1 answer -
(1 point) Differentiate y = y = -2e²u eu + e-u
(1 point) Differentiate \( y=\frac{-2 e^{2 u}}{e^{u}+e^{-u}} \). \[ y^{\prime}= \]1 answer -
1 answer
-
Evaluate the triple integral. \[ \iint y d V, \text { where } E=\{(x, y, z) \mid 0 \leq x \leq 8,0 \leq y \leq x, x-y \leq z \leq x+y\} \]1 answer -
1 answer
-
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\frac{\ln (7 x)}{x^{4}} \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]1 answer -
1 answer
-
f(x)=cos^(2)x-2sin x,quad0 <= x <= 2pi
2. \( f(x)=\cos ^{2} x-2 \sin x, \quad 0 \leq x \leq 2 \pi \)0 answers -
1 answer
-
Find the derivative of each function. ( \( 4 \mathrm{p} \) 1. \( f(x)=\frac{3 x^{2}}{2 x-1} \) \[ \begin{array}{l} f(x)=\frac{3 x^{2}}{2 x-1} \\ f^{\prime}(x)=\frac{d}{d x}\left(\frac{3 x^{2}}{2 x-1}\1 answer -
Given ƒ(x, y) = 5x³ – 2x²y¹ + y5, find fz(x, y) = 15x² - 4x4 2 fy(x, y) = -81²³+514 23 faz(x, y) = 30x - 4y fxy(x, y) = 16x³ 0° می ۔ X 0
Given \( f(x, y)=5 x^{3}-2 x^{2} y^{4}+y^{5} \), find \[ f_{x}(x, y \] \[ f_{y}(x, y)=-8 x^{2} y^{3}+5 y^{4} \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]1 answer