Calculus Archive: Questions from March 29, 2023
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(a) Let \( \boldsymbol{r}=x \boldsymbol{i}+y \boldsymbol{j}+z \boldsymbol{k} \) and \( r=|\boldsymbol{r}| \), verify each identity: \[ \nabla \cdot \boldsymbol{r}=3, \quad \nabla \cdot(r \boldsymbol{r2 answers -
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15. \( \int x^{2} \cos \left(x^{3}\right) d x= \) (A) \( -\frac{1}{3} \sin \left(x^{3}\right)+C \) (B) \( \frac{1}{3} \sin \left(x^{3}\right)+C \) (C) \( -\frac{x^{3}}{3} \sin \left(x^{3}\right)+C \)2 answers -
usa las trayectorias asignadas para verificar la no existencia del limite
Usa las trayectorias indicadas para verificar la no existencia del límite.2 answers -
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1) Utilice la definición de la derivada para hallar \( \frac{d y}{d x} \) para la función \( f(x)=-x^{2}+4 x+5 \). 2) Determine la ecuación de la línea tangente a la función \( f(x)=-x^{2}+4 x+52 answers -
Did I do it right?
\( \begin{array}{l}x^{3}+x y=\ln x y^{2}+y^{5}+1 \text {. Find } d y / d x \text { at the point }(1,-1) \\ 3 x+\left(x^{d y} y / d x+y\right)=1 / x y^{2}\left(x 2 y^{d y} / d x+y^{2}\right)+5 y^{4}+02 answers -
Hallar la derivada direccional de la funcion en P en direccion de V
4.1 Hallar la derivada direccional de la tunción en \( P \) en dirección de \( \vec{v} \). \[ z=f(x, y)=\sqrt{x^{2}+y^{2}} \text { en } P(3,4) ; \vec{v}=3 \vec{\imath}-4 \vec{\jmath} \text {. Ip } \2 answers -
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Can you please help with 24,34 and 40 !!!
15-48. Derivatives Find the derivative of the following functions. 15. \( y=\ln 7 x \) 16. \( y=x^{2} \ln x \) 17. \( y=\ln x^{2} \) 18. \( y=\ln 2 x^{8} \) 19. \( y=\ln |\sin x| \) 20. \( y=\frac{1+\2 answers -
3. Solve the non-homogeneous linear ODE with constant coefficients. (a) \( y^{\prime \prime}+9 y^{\prime}+20 y=6 e^{-2 x} \) (b) \( y^{\prime \prime}+2 y^{\prime}+5 y=5 x^{2} \) (c) \( y^{\prime \prim0 answers -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-12 y^{\prime \prime}+32 y^{\prime}=42 e^{x} \] \[ \begin{array}{l} y(0)=13, y^{\prime}(0)=30, y^{\prime \prime}(0)=17 \\2 answers -
( 1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-2 y^{\prime \prime}-y^{\prime}+2 y=0 \] \[ \begin{array}{l} y(0)=8, y^{\prime}(0)=-1, y^{\prime \prime}(0)=14 \\ y(x)= \2 answers -
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2. (10 points) Find \( d w / d t \) for \( w=x e^{y}+y \sin x-\cos z \) if \( x=2 t^{2}, y=t-1 \), and \( z=\pi t \).2 answers -
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38 and 40 please
In Exercises 27-60, find the minimum and maximum values of the function on the given interval by comparing values at the critical points and endpoints. 27. \( y=2 x^{2}+4 x+5, \quad[-2,2] \) 28. \( y=2 answers -
Use the Chain Rule to find \( d w / d t \). \[ w=\ln \sqrt{x^{2}+y^{2}+z^{2}}, \quad x=3 \sin t, \quad y=6 \cos t, \quad z=7 \] \[ \frac{d w}{d t}= \]2 answers -
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Find the general solution of (1) \( y^{\prime \prime \prime}-4 y^{\prime \prime}=48 x^{2}+48 x+22 \) (2) \( x^{2} y^{\prime \prime}-2 x y^{\prime}+2 y=x^{3} \ln x \) (3) \( y^{\prime \prime}-25 y=2 x2 answers -
Find the following limit. \[ \lim _{(x, y) \rightarrow(0,8)} \arctan \left(\frac{x^{2}+28}{x^{2}+(y-8)^{2}}\right) \]2 answers -
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delta y
Table 6.3 \begin{tabular}{|c|l|c|c|} \hline Mass \( (\mathrm{Kg}) \) & Scale \( y_{\mathrm{i}}(\mathrm{m}) \) & \( \mathrm{F}=m g(\mathrm{~N}) \) & \( \Delta y=\left|y_{i+1}-y_{i}\right|(m) \) \\ \hli2 answers -
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(2) Evaluate the double integral \[ \iint_{D} y \sqrt{x^{2}-y^{2}} d A, \] where \( D=\{(x, y): 0 \leq x \leq 2,0 \leq y \leq x\} \).2 answers -
Objetivo: Esta actividad tiene como propósito ayudar al estudiante a resolver problemas de optimización. (Objetivo 5) Instrucciones al estudiante: En la siguiente actividad usted resolverá el ejerc2 answers -
Differentiate the following function. \[ f(x)=\frac{e^{x}+\tan (x)}{\cos (x)} \] A) \( f^{\prime}(x)=\frac{\left(e^{x}+\cot ^{2}(x)\right)-\sin (x)\left(e^{x}+\tan (x)\right)}{\cos (x)} \) B) \( f^{\p2 answers -
Produce the equation of the line tangent of the given function at the specified point. \[ y=x^{2} e^{x} ; \quad P(1, e) \] A) \( y=(2 e) x-3 e^{2}+1 \) B) \( y=(3 e) x-3 e^{2}+1 \) C) \( y=\left(x^{2}2 answers -
number 10 please
9-12 Find the Jacobian \( \partial(x, y, z) / \partial(u, v, w) \). 9. \( x=3 u+v, y=u-2 w, z=v+w \) 10. \( x=u-u v, y=u v-u v w, z=u v w \)2 answers -
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\( (30 / 30) \) Problem 4. Find \( \frac{d y}{d x} \) : (i) \( y=\frac{\left(e^{x}+\sqrt{x}\right)^{3}}{\sqrt{x^{2}+1}} \). (ii) \( y=\tan ^{-1}(\ln (x)) \) (iii) \( y=e^{\sin ^{-1}(x)} \)2 answers -
Una catedral está situada en una colina, como se ve en la figura. Cuando la cima de la torre se ve desde la base de la colina, el ángulo de elevación es \( 50^{\circ} \); cuando se ve a una distanc2 answers -
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laplace transform
Using LAPlace solve \[ \begin{array}{ll} y^{\prime \prime}-2 y^{\prime}+y=e^{t}+t & y(0)=1 \\ y^{\prime}(0)=0 \end{array} \]2 answers -
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pls help
oblem \# 1: Find the domain of the function \( f(x, y)=\ln \left(2 x^{2}+6 y+1\right) \). The set of all ordered pairs \( (x, y) \) for which: (A) \( y \leq-\frac{1+2 x^{2}}{6} \) (B) \( y-\frac{1+2 x2 answers -
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(b) Given \( \frac{d}{d x} f(x)=\frac{1}{x}-e^{x} \sin \left(c^{x}\right) \), find a possible \( f(x) \). (c) Given \( \frac{d}{d x} f(x)=\frac{x^{4}+4 x^{2}-1}{\left(x^{2}+1\right)^{2}} \), find a po2 answers -
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Optimiza la funcion sujeta a la segunda funcion y encuentra los 4 puntos criticos utilizando los Multiplicadores de Lagrange
Optimización: \( \quad \frac{3}{125} x^{2}-\frac{1}{45} y^{2}+25 \) s vjeta a: \( \left(\frac{3}{125}+0.2\right) x^{2}+\left(-\frac{1}{45}+0.2\right) y^{2}=15 \)2 answers -
encuentra el valor de x, y y del multiplicador de langrange resolviendo el sistema de ecuaciones
\( \left.\begin{array}{l}\alpha x=\frac{6}{125} x-\frac{6}{125} x \lambda-0.4 x \lambda \\ \alpha y=-\frac{2}{45} y+\frac{2}{45} y \lambda-0.2 y \lambda \\ \alpha \lambda=-\frac{3}{125} x^{2}-0.2 x^{20 answers -
V. Cada lado de un cuadrado astá creciendo a una tasa de \( 6 \mathrm{~cm} / \mathrm{s} \). ¿Cuál es la tasa de cambío del área del cuadrado cuando esta es \( 16 \mathrm{~cm}^{2} ? \) (8 puutos)2 answers -
VI. El movimiento de una partícula se puede describir con la ecuación \( f(t)=t^{3}-12 t^{2}+36 t \). Determine cuando la partícula se mueve hacia la izquierda y desacelera (10 puntos). The movemen2 answers -
Optimización: \( \underbrace{\frac{3}{125} x^{2}-\frac{1}{45} y^{2}+25} \) sujeta a: \( \underbrace{\left(\frac{3}{125}+0.2\right) x^{2}+\left(-\frac{1}{45}+0.2\right) 4^{2}=15} \) ecuacion del techo0 answers -
Problem 3. Compute the following integrals. 1. \( \int_{0}^{2 \sqrt{2 x-x^{2}}} \int_{0} 5 \sqrt{x^{2}+y^{2}} d y d x \) 2. \( \int_{0}^{4} \int_{x}^{4} \sin \left(y^{2}\right) d y d x \) 3. \( \int_{2 answers -
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Find \( F(x) \) if \( F^{\prime}(x)=\sin ^{3}(6 x) \) and \( F\left(\frac{\pi}{6}\right)=1 \). \[ \begin{array}{l} F(x)=\frac{1}{24} \sin ^{4} 6 x+1 \\ F(x)=\frac{1}{6} \cos ^{3} 6 x+\frac{1}{6} \cos2 answers -
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The domain of \[ f(x, y)=\frac{\sqrt{x-15}}{\ln (y-4)-5} \] is the set of all ordered pairs \( (x, y) \) of real numbers such that: NOTE: ONLY 2 ANSWER TRIES ON THIS PROBLEM. \[ \begin{array}{l} \{(x,2 answers -
1. Determine the limit, if it does not exist, explain why. PLEASE ONLY THE FIRST PART!!
I. Determine el limite, en caso de que no exista explique por qué. a) \( \lim _{(x, y) \rightarrow(0,1)} \frac{\arccos (x / y)}{1+x y} \) b) \( \lim _{(x, y) \rightarrow(0,0)} \frac{x-y}{\sqrt{x}+\sq2 answers -
I. Halle el diferencial total a) \( z=e^{x} \operatorname{sen}(y) \) b) \( w=\frac{x+y}{z-3 y} \) II. Considere la función \( f(x, y)=y e^{x} \) y traktaje: a) Evaluar \( f(2,1) \) y \( f(2.1,1.05) \2 answers -
(2 points) Calculate all four second-order partial derivatives of \( f(x, y)=3 x^{2} y+8 x y^{3} \). \[ f_{2 x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y \] (2 points) Calcu2 answers -
l. Analice la continuidad de la función a) \( f(x, y, z)=\frac{z}{x^{2}+y^{2}-4} \) b) \( f(x, y)=\left\{\begin{array}{c}\frac{\operatorname{sen}(x y)}{x y}, x y \neq 0 \\ 1, x y=0\end{array}\right.2 answers -
II. Considere la función \( f(x, y)=y e^{x} \) y trathaje: a) Evaluar \( f(2,1) \) y \( f(2.1,1.05) \) b) Calcular \( \Delta z=f(x+\Delta x, y+\Delta y)-f(x, y) \) c) usar el diferencial total \( d z2 answers -
Evaluate and simplify y′ (find derivative of y)
15. \( y=\left(1+x^{4}\right)^{3 / 2} \) 18. \( y=5 x+\sin ^{3} x+\sin x^{3} \)2 answers -
Find \( \frac{d y}{d x} \) of \( y=\left(3 x^{2}-2\right) \sin ^{2} x \) Select one: a. \( 6 x \sin ^{2} x+2\left(3 x^{2}-2\right) \sin x \) b. \( 6 x \sin ^{2} x+\left(3 x^{2}-2\right) \sin x \cos x2 answers -
Calculate the double integral. \[ \iint_{R} \frac{9\left(1+x^{2}\right)}{1+y^{2}} d A, R=\{(x, y) \mid 0 \leq x \leq 3,0 \leq y \leq 1\} \]2 answers -
Find the quadratic approximation to the function \( f(x, y)=\cos x \cos y \) valid near the origin. \[ \begin{array}{l} f(x, y)=1-\frac{x^{2}}{4}-\frac{y^{2}}{4} \\ f(x, y)=1-\frac{x^{2}}{2}-\frac{y^{2 answers -
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Sketch the graph of a twice-differentiable function \( y=f(x) \) with the properties given in the table. Choose the correct graph below.2 answers -
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number 10 please
In Problems 1-18 solve each differential equation by variation of parameters. 1. \( y^{\prime \prime}+y=\sec x \) 2. \( y^{\prime \prime}+y=\tan x \) 3. \( y^{\prime \prime}+y=\sin x \) 4. \( y^{\prim2 answers -
45 and 47 pls
45-56 Use logarithmic differentiation to find the derivative of the function. 45. \( y=\left(x^{2}+2\right)^{2}\left(x^{4}+4\right)^{4} \) 46. \( y=\frac{e^{-x} \cos ^{2} x}{x^{2}+x+1} \) 47. \( y=\sq2 answers -
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Sea \( f(x, y)=\frac{-5 y}{x} \) Resuelve la ecuación diferencial \( y^{\prime}=f(x, y) \) con valor inicial \( y(2)=16 \).2 answers