Calculus Archive: Questions from March 23, 2023
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9 and 10 pls
In Exercises 5-12, find and sketch the domain for each function. 5. \( f(x, y)=\sqrt{y-x-2} \) 6. \( f(x, y)=\ln \left(x^{2}+y^{2}-4\right) \) 7. \( f(x, y)=\frac{(x-1)(y+2)}{(y-x)\left(y-x^{3}\right)2 answers -
2 answers
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2 answers
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Let \( y \) be the solution of IVP \( y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=0, y(0)=1, y^{\prime}(0)=0, y^{\prime \prime}(0)=1 \). Then \( y(-1)= \) a. \( -e \) b.e c. \( 2 e \)2 answers -
2 answers
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puntos) Determine la ecuación de aquella curva que es solución de la ecuacion erencial \( \sqrt{1-x^{2}} y^{\prime}-\sqrt{1-y^{2}}=0 \) que pasa por el punto \( (0, \sqrt{3} / 2) \)2 answers -
\( \begin{array}{l}p=3 x+6 y+3 z+6 w+3 v \text { subjec } \\ x+y \leq 4 \\ y+z \leq 4 \\ z+w \leq 12 \\ w+v \leq 16 \\ x \geq 0, y \geq 0, z \geq 0, w \geq 0, v \geq 0 \\\end{array} \)2 answers -
2. (15 puntos) Determine la solución general de la ecuación diteremiciai cus(y) \( y \sin (x)=1 \) (15 puntos) La ecuación diferencial \( T^{\prime}=k S\left(T-T_{m}\right) \), con \( k0 \) constan2 answers -
2 answers
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58-61. Absolute extrema on open and/or unbounded regions If possible, find the absolute maximum and minimum values of the following functions on the region \( R \). 58. \( f(x, y)=x+3 y ; R=\{(x, y):|3 answers -
Calculate the double integral. \[ \iint_{R} x \sec ^{2}(y) d A, \quad R=\left\{(x, y) \mid 0 \leq x \leq 8,0 \leq y \leq \frac{\pi}{4}\right\} \]2 answers -
3. Determine the derivative of each function below, simplify fully. a) \( y=\sqrt{x^{2}+\sin 3 x} \) \( y=\left(\frac{4 x^{2}+1}{3 x-2}\right)^{5} \) c) \( y=\sin \left(\cos x^{2}\right) \) \[ \text {2 answers -
29 and 30
In Exercises 23-34, find \( f_{x}, f_{y} \), and \( f_{z} \). 23. \( f(x, y, z)=1+x y^{2}-2 z^{2} \) 24. \( f(x, y, z)=x y+y z+x z \) 25. \( f(x, y, z)=x-\sqrt{y^{2}+z^{2}} \) 26. \( f(x, y, z)=\left(2 answers -
42 abd 45
Calculating Second-Order Partial Derivatives Find all the second-order partial derivatives of the functions in Exercises 41-50. 41. \( f(x, y)=x+y+x y \) 42. \( f(x, y)=\sin x y \) 43. \( g(x, y)=x^{22 answers -
2 answers
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2 answers
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what is the best answer
for \( y: \frac{d y}{d x}=e^{y} \sin x \) A. \( y=e^{\cos x}+C \) B. \( y=e^{-\cos x}+C \) C. \( y=\ln |\cos x+C| \) D. \( y=-\ln |\cos x+C| \) E. \( y=-\ln |\cos x|+C \)2 answers -
what is the best answer
Solve for \( y \) if \( \frac{d y}{d x}=(x y)^{2} \) and \( y(0)=1 \) A. \( y=\frac{-3}{x^{3}-3} \) B. \( y=\frac{-3}{x^{3}+1} \) C. \( y=\frac{2}{x^{3}+2} \) D. \( y=\frac{-2}{x^{3}+2} \) E. \( y=\fr2 answers -
2 answers
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2 answers
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2 answers
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Let \( y \) be the solution of IVP \( y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=0, y(0)=1, y^{\prime}(0)=0, y^{\prime \prime}(0)=1 \). Then \( y(-1)= \) a. \( -e \) b.e c. \( 2 e \)2 answers -
2 answers
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only question 7, 13, 17,19 needed. Please show the steps clearly.
7. \( \lim _{(x, y) \rightarrow(\pi, \pi / 2)} y \sin (x-y) \) 9. \( \lim _{(x, y) \rightarrow(0,0)} \frac{x^{4}-4 y^{2}}{x^{2}+2 y^{2}} \) 11. \( \lim _{(x, y) \rightarrow(0,0)} \frac{y^{2} \sin ^{2}2 answers -
Calculate the double integral. \[ \iint_{R} x \sec ^{2}(y) d A, \quad R=\left\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq \frac{\pi}{4}\right\} \]2 answers -
2 answers
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12. \( f(x, y)=(x+y)(x y+1) \) 4. \( \int_{D}\left(y^{3}+y^{5}\right) d A \) 7. \( \int_{B}\left(y-y^{3}\right) d A \)2 answers -
help me solve these
2. \( f(x, y)=2 x y, 5 x+4 y=100 \) 3. \( f(x, y, z)=x y z, x^{2}+y^{2}+4 z^{2}=12 \)0 answers -
Differentiate \[ \begin{array}{l} f(x)=3 \sin x-2 \cos x \\ y=2 \sec x-\csc x \\ y=\sec \theta \tan \theta \\ f(\theta)=\frac{\sin \theta}{1+\cos \theta} \\ H(t)=\cos ^{2} t \end{array} \]2 answers -
Solve The following differential equations Q1) \( y^{\prime} \sin (2 \pi x)=\pi y \sin (2 \pi x) \) Q2) \( (2 x y-\tan y) d x+\left(x^{2}-x \sec ^{2} y\right) d y=0 \) Q3) \( (x+2) \sin y d x+x \cos y2 answers -
Evaluate the double integral. \[ \begin{array}{l} \iint_{D}(2 x+y) d A, \quad D=\{(x, y) \mid 1 \leq y \leq 2, y-1 \leq x \leq 1\} \\ -\frac{19}{6} \end{array} \]2 answers -
Integración de potencias de funciones trigonométrica CONTESTAR POR LA REGLA DE LA POTENCIA
\( \int \operatorname{sen}^{2}(2 x) \cos ^{7}(2 x) d x \) \( \int \operatorname{sen}^{3}(x) \cdot \cos ^{5} x d x \) \( \int \sin (2 x) \cos (4 x) d x \)2 answers -
2 answers
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2 answers
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El siguiente es una lista de ejercicios sobre derivadas parciales. Determine las derivadas parciales de las siguientes funciones en los puntos dados
1. Determine las derivadas parciales de las siguientes funciones en los puntos dados: a) \( f(x, y)=\cos (x y) e^{5 x+2 y} \) en \( (2,2) \). c) \( f(x, y)=\frac{3 x+2 y}{x y} \) en \( (1,2) \). b) \(2 answers -
El siguiente es una lista de ejercicios sobre derivadas parciales. Sean f(x, y, s,w) = e2x+3y−2s−5w y r(t) = (cost,sen t, cost,sen t). Utilice la regla de la cadena para calcular dzdt (en función
1. Sean \( f(x, y, s, w)=e^{2 x+3 y-2 s-5 w} \) y \( \mathbf{r}(t)=(\cos t, \operatorname{sen} t, \cos t, \operatorname{sen} t) \). Utilice la regla de la cadena para calcular \( \frac{d z}{d t} \) (e2 answers -
oblem \# 4: What is the domain of the function \( f(x, y)=x^{3} y^{1 / 7}-8 \ln x \) ? (A) \( \{(x, y): x \geq 0, y>0\} \) (B) \( \{(x, y): x>0\} \) (C) \( \{(x, y): x>0, y>0\} \) (D) \( \{(x, y): x>02 answers -
2 answers
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2 answers
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Please help :(
5. Find the derivatives: a) \( y=\cos 4 e^{2 x} \) b) \( y=\sin \left(\ln 4 x^{3}\right) \) c) \( y=-3 e^{3 x^{2}+5} \) d) \( y=\ln \left(x^{4}+5 x^{2}\right)^{\frac{3}{2}} \)2 answers -
solve the following differential equations
Q2) \( (2 x y-\tan y) d x+\left(x^{2}-x \sec ^{2} y\right) d y=0 \) Q3) \( (x+2) \sin y d x+x \cos y d y=0 \) Q4) \( y^{\prime}+2 x y=2 x^{2} e^{-x^{2}}+\frac{y}{x} \)2 answers -
(d) If \( z=\sin (3 x+2 y) \), show that \( 3 \frac{\partial^{2} z}{\partial y^{2}}-2 \frac{\partial^{2} z}{\partial x^{2}}=6 z \)2 answers -
Find the gradient of each of the following functions: (a) \( f(x, y)=x e^{x y} \) (b) \( f(x, y)=3 x^{2}-x y+y \) (c) \( f(x, y)=(x+y) e^{x-y} \) (d) \( f(x, y, z)=x^{2} y+y^{2} z+z^{2} x \)2 answers -
3. [24 pts] Calculate the derivative of the following functions. (a) \( y=e^{-x^{2}+7 x+2} \) (c) \( y=\log _{3}(5-4 x) \) (b) \( y=\ln \left(3 x^{2}+2 x-7\right) \) (d) \( y=10^{x^{3}+2 x+1} \)2 answers -
2 answers
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Evaluate the double integral. \[ \iint_{D} 4 x d A, D=\{(x, y) \mid 0 \leq x \leq \pi, 0 \leq y \leq \sin x\} \]3 answers -
I. If \( y=\tan ^{-1}(\cos x) \), then \( y^{\prime}= \) (A) \( \frac{\sin x}{1+\cos ^{2} x} \) (B) \( -\frac{\cos x}{1+\sin ^{2} x} \) (C) \( -\frac{\sin x}{1+\cos ^{2} x} \) (D) \( \frac{\cos x}{1+\2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\sin \left(x^{2}\right) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]2 answers -
4 answers
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Evaluate \( \iint_{R} x y^{2} d x d y \) where \( R=\{(x, y):-2 \leq x \leq 1,0 \leq y \leq 1\} \) a. -2 b. \( -1 / 2 \) c. 1 d. \( 3 / 2 \) e. 32 answers