Calculus Archive: Questions from February 05, 2023
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Given w = 3x + y 2 + z 3 where x = e rs2 , y = ln r + s t and z = rst2 . Find ∂w ∂s .
b) Given \( w=3 x+y^{2}+z^{3} \) where \( x=e^{r s^{2}}, y=\ln \left(\frac{r+s}{t}\right) \) and \( z=r s t^{2} \). Find \( \frac{\partial w}{\partial s} \).2 answers -
Find the derivative. \[ \begin{aligned} y= & 3-5 x^{3} \\ & 3-15 x^{2} \\ & -15 x \\ & -15 x^{2} \\ & -10 x^{2} \end{aligned} \]2 answers -
Find \( y^{\prime} \). \[ \begin{aligned} y= & \left(4 x^{3}+9\right)\left(2 x^{7}-3\right) \\ & 80 x^{9}+126 x^{6}-36 x^{2} \\ & 16 x^{9}+126 x^{6}-36 x \\ & 16 x^{9}+126 x^{6}-36 x^{2} \\ & 80 x^{9}2 answers -
1. \( y=5 x^{2} \). Find \( \frac{\partial y}{\partial x} \). 2. \( y=12 x^{3}+3 z \). Find \( \frac{\partial y}{\partial x} \). 3. \( y=5 z \). Find \( \frac{\partial y}{\partial x} \). 4. \( y=2 x^{2 answers -
Resuelva: 1. Encuentre la ecuación del plano determinado por los puntos \( P(1,2,3) \) \[ Q(2,3,1) \quad R(0,-2,-1) \] 2. Encuentre las ecuaciones paramétricas y simétricas para la linea que pasa p2 answers -
Situacion: Dadas las coordenadas de los puntos \( P(-1,-2,3) Q(-2,3,5) \) y \( R(4,5,6) \) hallar: a. Los vectores \( \overrightarrow{P Q} \) y \( \overrightarrow{P R} \) b. \( \overrightarrow{P Q} \t2 answers -
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e the IVP: \( y^{\prime}=2 y, \quad y(0)=3 \) \[ y=3 e^{2 x} \] \[ y=A e^{2 x} \] \[ y=A \] \[ y=e^{2 x+c} \]2 answers -
Find \( f_{x}(x, y) \) \[ \begin{array}{l} f(x, y)=e^{-4 x y} \\ f_{x}(x, y)=-4(x+y) e^{-4 x y} \\ f_{x}(x, y)=-4 e^{-4 x y} \\ f_{x}(x, y)=-4 y e^{-4 x} \\ f_{x}(x, y)=-4 y e^{-4 x y} \end{array} \]2 answers -
\( \begin{array}{c}\int\left(\tan \left(\frac{x}{10}\right)\right)^{5} d x \\ \frac{1}{10} \tan ^{4}\left(\frac{x}{10}\right)-\tan ^{2}\left(\frac{x}{10}\right)-10 \ln \left|\cos \left(\frac{x}{10}\ri2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ x^{2}+y^{2}=4, \quad 0 \leq z \leq 4 ; \quad f(x, y, z)=e^{-z} \]2 answers -
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2. Dados los vectores \( \vec{A}=i+2 j+3 k \) y \( \vec{B}=2 i+j-5 k \) Determina: a. \( C_{\vec{B}} \vec{A} \) b. \( \operatorname{Proj}_{\vec{B}} \vec{A} \) c. La componente veclorial del vector \(2 answers -
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1. \( y=x^{7} \) 2. \( y=x^{8} \) 3. \( y=-3 x \) 4. \( y=-0.5 x \) 5. \( y=12 \) 6. \( y=7 \) 7. \( y=2 x^{15} \) 8. \( y=3 x^{10} \) 9. \( y=x^{-6} \) 10. \( y=x^{-8} \) 11. \( y=4 x^{-2} \) 12. \(2 answers -
Find the vertical asymptote ecuation of:
Halle la ecuación de la asintota vertical de \( f(x)=\frac{x^{2}+3 x+2}{x^{2}+4 x+3} \)2 answers -
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Find the partial derivatives \( f_{x} \) and \( f_{y} \) if \( f(x, y)=13 x^{2} y^{3}+7 x y^{2}-5 x^{2} \). \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]2 answers -
Find the limit of:
Halle el \( \lim _{x \rightarrow 4} \frac{\sqrt{x}+5}{6-\sqrt{x}} \) Halle el \( \lim _{x \rightarrow 1} \frac{x-1}{\sqrt{5-x}-2} \)2 answers -
utilice el teorema de criterio de analiticidad para demostrar que la función indicada es analítica en un dominio adecuado.
\( f(z)=e^{x} \cos y+i e^{x} \operatorname{sen} y \) \( f(z)=e^{x^{2}-y^{2}} \cos 2 x y+i e^{x^{2}-y^{2}} \operatorname{sen} 2 x y \) \( f(z)=\frac{x-1}{(x-1)^{2}+y^{2}}-i \frac{y}{(x-1)^{2}+y^{2}}2 answers -
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exprese la cantidad indicada en la forma a+ib
3. \( \operatorname{sen}\left(\frac{\pi}{4}+i\right) \) 11. \( \operatorname{senh}\left(1+\frac{\pi}{3} i\right) \)2 answers -
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For the following exercises, graph the equations and shade the area of the region between the curves. Determine its area by integrating over the \( x \)-axis. 11. \( y=e^{x}, y=e^{-x}, x=-1 \) and \(2 answers -
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