Calculus Archive: Questions from December 15, 2022
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1. Solve the given initial value problem. (a) \[ \mathbf{y}^{\prime}=\left[\begin{array}{ll} -2 & 1 \\ -5 & 4 \end{array}\right] \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{l} 1 \\ 3 \end{arra2 answers -
Encuentre un valor de la constante \( k \), si es posible, en el que \( f(x)=\left\{\begin{array}{ll}k x^{2} & x \leq-3 \\ -7 x+k & x>-3\end{array}\right. \) es continuo en todas partes. Seleccione un2 answers -
Encuentra los números, si los hay, donde la función \( f(x)=\left\{\begin{array}{cc}3 x-2 & \text { si } x \leq 1 \\ 0 & \text { si } x>1\end{array}\right. \) es discontinua. Seleccione una: a. \( -2 answers -
93. Los inhibidores de la enzima convertidora de angiotensina (ECA) son un tipo de medicamento para la presión arterial que reduce la presión arterial al dilatar los vasos sanguíneos. Suponga que e0 answers -
Evaluate the following triple integrals: a) \( \quad \int_{1}^{2} \int_{0}^{2 z} \int_{0}^{\ln x} x e^{-y} d y d x d z \) b) \( \iiint_{E} 2 x d V, E=\left\{(x, y, z) \mid 0 \leq y \leq 2,0 \leq x \le2 answers -
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Help ASAP! Please
Find the limit. \[ \lim _{y \rightarrow \infty}\left(\frac{3 y+\sqrt{y^{2}+2 y}}{y}\right) \]2 answers -
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Evaluate \( \iiint_{\mathcal{B}} f(x, y, z) d V \) for the specified function \( f \) and \( \mathcal{B} \) : \[ f(x, y, z)=\frac{z}{x} \quad 2 \leq x \leq 6,0 \leq y \leq 7,0 \leq z \leq 4 \] \[ \iii2 answers -
Evaluate \( \iiint_{\mathcal{W}} f(x, y, z) d V \) for the function \( f \) and region \( \mathcal{W} \) specified: \[ f(x, y, z)=42(x+y) \quad \mathcal{W}: y \leq z \leq x, 0 \leq y \leq x, 0 \leq x2 answers -
For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=x^{3}+7 x^{2} y^{2}-5 y^{3}-x+y \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers -
For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=54 x^{1 / 2} y^{1 / 3}+7 \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers -
For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=600 x^{0.05} y^{0.02} \] (a) \( f_{x}(x, y) \)2 answers -
For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=(x+y)^{-2} \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers -
For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=\ln \left(x^{4}+y^{3}\right) \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers -
1. Determine the limit, in case that does not exist explain why. 2. Analize the continuity of the function.
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 -
Analyze the continuity of the function Analyze the continuity of the fuction
II. 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 -
Evaluate the double integral. \[ \iint_{D} \frac{y}{x^{2}+1} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq \sqrt{x}\} \]2 answers -
Evaluate the triple integral. \[ \iiint_{E} y d V, \text { where } E=\{(x, y, z) \mid 0 \leq x \leq 4,0 \leq y \leq x, x-y \leq z \leq x+y\} \]2 answers -
Halle la integral indefinida: \[ \int\left(x^{5 / 4}-8 x-7\right) d x \] a. \( \frac{4}{9} x^{9 / 4}-8 x^{2}-7 x+C \) b. \( \frac{4}{9} x^{9 / 4}-4 x^{2}+C \) c. \( \frac{4}{9} x^{9 / 4}-4 x^{2}-7 x+C2 answers -
\( -8 \) Use the Chain Rule to find \( d z / d t \) or \( d w / d t \). 3. \( z=x y^{3}-x^{2} y, \quad x=t^{2}+1, \quad y=t^{2}-1 \) 4. \( z=\frac{x-y}{x+2 y}, \quad x=e^{\pi r}, \quad y=e^{-\pi t} \)2 answers -
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Halle una ecuación de la recta tangente a la gráfica de la función: \( f(x)=x^{3}+4 x^{2} \) en el punto: \( (-2,8) \) a. \( y=-4 x-7 \) b. \( y=-4 x \) c. \( y=-4 x+16 \) d. \( y=4 x-16 \) Halle2 answers -
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Given \( f(x, y)=-5 x^{5}-2 x y^{2}+y^{4} \), find the following numerical values: \[ f_{x}(3,3)= \] \[ f_{y}(3,3)= \]2 answers -
Differentiate the function \[ y=e^{\operatorname{con}(2 x)} \] \[ \begin{array}{l} y^{\prime}=-2 \sin (2 x) e^{\cos (2 x)} \\ y^{\prime}=2 \sin (2 x) e^{\cos (2 x)} \\ y^{\prime}=-2 \sin (2 x) e^{\cos2 answers -
Parte I: Halle las ecuaciones simétricas de la recta normal a la superficie en el punto dado 1. \( x^{2}+y^{2}+z^{2}=9,(3,3,3) \) 2. \( z=x^{2}-y^{2},(3,2,5) \) 3. \( x y z=10,(1,25) \) 4. \( x y-z=02 answers -
Need it ASAP, 30 mins. Will leave a thumbs up
2. Find the directional derivative of \( f(x, y)=x \cos y \) in the direction of \( \mathbf{v}=\langle 2,-1\rangle \). A. \( \frac{1}{\sqrt{5}}(2 \cos y+x \sin y) \) B. \( \frac{1}{\sqrt{5}}(2 \sin y-2 answers -
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5.4
Evaluate \( \iiint_{E}(x+y-5 z) d V \) where \[ E=\left\{(x, y, z) \mid-2 \leq y \leq 0,0 \leq x \leq y, 02 answers -
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 -
\( \frac{d}{d x} \int_{0}^{\sin x} \frac{d t}{1+t^{2}} \) \( \frac{1}{1+\sin ^{2} x} \) \( \frac{\sin x}{1+\sin ^{2} x} \) \( -\frac{\cos x}{1+\sin ^{2} x} \) \( \frac{\cos x}{1+\sin ^{2} x} \)2 answers -
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