Calculus Archive: Questions from April 12, 2023
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Determine el valor exacto de arcsin(sin[11pi/6]) y arctan(tan[11pi/4]). por favor muestra tu trabajo1 answer
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Let \( \frac{d y}{d x}=7 x^{-2}+4 x^{-1}-4 \). Find \( y \) if \( y(1)=9 \) \[ y=-7 x^{-1}+4 \ln (|x|)-4 x+17 \]2 answers -
\[ \lim _{(x, y) \rightarrow(0,0)} \frac{x y}{3 x^{2}+2 y^{2}}= \] Seleccione una: a. 0 b. No existe c. \( \frac{1}{5} \) d. \( \frac{1}{3} \)2 answers -
Solve the following system:
\( \begin{array}{l}5 x^{\prime}+y^{\prime}-5 x-y=0 \\ 4 x^{\prime}+y^{\prime}-3 x=t, \quad x(0)=1 \text { and } y(0)=0\end{array} \)2 answers -
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El dominio de la función \( f(x, y)=\sqrt{16-x^{2}-y^{2}} \) es: Seleccione una: a. \( \left\{(x, y): x^{2}-y^{2} \leq 4^{2}\right\} \) b. \( \left\{(x, y): x^{2}+y^{2} \leq 1\right\} \) c. \( \left\2 answers -
Evaluate \( \iiint_{\mathcal{B}} f(x, y, z) d V \) for the specified function \( f \) and \( \mathcal{B} \) : \[ f(x, y, z)=\frac{z}{x} \quad 2 \leq x \leq 16,0 \leq y \leq 3,0 \leq z \leq 4 \] \[ \ii2 answers -
2) Determine la derivada de las siguientes funciones: \[ y=8 \sqrt{x}+\frac{7}{x^{2}}+4 \quad(x>0) \] \[ f(x)=\sin x \cot x \] \[ f(x)=\left(x^{5}+2\right) \cos x \] \[ 5 x^{2} y^{3}-6 x+3 y=11 \]2 answers -
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\( \lim _{x \rightarrow 0} \frac{3 \sin 4 x}{\sin 3 x} \) 2. Determine \( \frac{d y}{d x} \) for each of the following: a. \( y=10^{x} \) c. \( y=(5 x)\left(5^{x}\right) \) e. \( y=\frac{4 x}{4^{x}}2 answers -
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1. Differentiate each of the following: a. \( y=6-e^{x} \) d. \( y=e^{-3 x^{2}+5 x} \) b. \( y=2 x+3 e^{x} \) e. \( y=x e^{x} \) c. \( y=e^{2 x+3} \) f. \( s=\frac{e^{t}-1}{e^{t}+1} \)2 answers -
Determine the volume of a balloon by integration; For this, consider that an ovoid can be obtained by rotating around the X axis the upper part of an ellipse with a major axis of 27 cm and a minor axi
Balón de americano (ovoide). Determine el volumen de un balón mediante integración; para esto considere que un ovoide se puede obtener rotando en tomo al eje \( X \) la parte superior de una elipse2 answers -
Evaluate \( \iiint_{\mathcal{W}} f(x, y, z) d V \) for the function \( f \) and region \( \mathcal{W} \) specified: \[ f(x, y, z)=18(x+y) \quad \mathcal{W}: y \leq z \leq x, 0 \leq y \leq x, 0 \leq x2 answers -
5. (8 points) Calculate \( \frac{d y}{d x} \). You need not expand your answer. \[ y=\frac{42 x^{-0.8}-0.6 x^{-0.5}}{0.4+x^{0.1}} \] a. \( \frac{\left(-3.36 x^{-18}+0.3 x^{-15}\right)\left(0.4+x^{0.1}2 answers -
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Differentiate the function. \[ \begin{array}{r} y=(\ln x+9)^{2}+\left(e^{x}+5\right)^{2} \\ y^{\prime}=2 \frac{\ln x+9}{x}+2 e^{x}\left[e^{x}+5\right] \end{array} \]2 answers -
I. Considere \( w=x^{2}-2 x y+y^{2}, x=r+\theta, y=r-\theta \) para determinar \( \frac{\partial w}{\partial r} \& \frac{\partial w}{\partial \theta} \). II. Considere \( w=x y \cos (z), x=t, y=t^{2}2 answers -
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please Answer 6.4.4 and 6.4.8 please
Evaluate the iterated integrals: 6.4.3. \( \int_{0}^{2} \int_{0}^{1} \int_{-1}^{0}\left(x^{2}+y^{2}+z^{2}\right) d z d y d x \). 6.4.4. \( \int_{-2}^{3} \int_{0}^{1} \int_{0}^{2}\left(x e^{y}+y e^{z}\2 answers -
\( F(x)=\int_{6}^{e^{x}}\left(y^{4} \sin (y)\right) d y \), find \( F^{\prime}(x) \) \( F^{\prime}(x)= \)2 answers -
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Let \( \frac{d y}{d x}=7 x^{-2}+4 x^{-1}-6 \). Find \( y \) if \( y(1)=1 \) \[ y=-\frac{7}{x}+4 \ln (|x|)-6 x-12 \]2 answers -
\#1. Compute the sum, if possible. If not possible, explain why. \[ \sum_{n=0}^{\infty} \frac{3-7^{n}}{14^{n}} \]2 answers -
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