Calculus Archive: Questions from February 24, 2023
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Evaluate the double integral. \[ \iint_{D} 8 y \sqrt{x^{2}-y^{2}} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 1,0 \leq y \leq x\} \]2 answers -
2 answers
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only the highlighted please
9-26 Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Table 1.2.3, and then applying the appropriate transformations. 9. \(2 answers -
2 answers
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1. \( \lim _{x \rightarrow 2}(2-x) \) 2. \( \lim _{x \rightarrow 2}(8+\sqrt{8 x}) \) 3. \( \lim _{x \rightarrow 1} \frac{\left(x^{2}-1\right)}{x-1} \) 4. \( \lim _{\Delta x \rightarrow 0} \frac{(x+\De2 answers -
2 answers
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please solve (c), (d), (m),(v), and (w)
1. Find the following derivatives: (a) \( f(x)=\left(5 x^{6}+2 x^{3}\right)^{4} \) (m) \( y=\sqrt{\frac{x}{x+1}} \) (b) \( f(x)=\sqrt{5 x+1} \) (n) \( y=e^{\tan \theta} \) (c) \( F(x)=\left(1+x+x^{2}\2 answers -
Exercise 5 Solve the IVP \[ y^{\prime \prime}+4 y^{\prime}+5 y=\delta(t-1), \quad y(0)=0, y^{\prime}(0)=3 \]2 answers -
d. \( y=[\cos (x)]^{\sin (x)} \). e. \( y=\frac{\cos ^{-1}(x)}{\sqrt{1-x^{2}}} \) f. \( y=\log _{3}(x)+\sqrt{1-x^{2}} \operatorname{sech}^{-1}(x) \)0 answers -
2 answers
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(4) Find the extreme values of \( f(x, y)=2 x^{2}-4 y^{2} \) on the square \( 0 \leq x \leq 1,0 \leq \) \( y \leq 1 \).2 answers -
Utiliza la siguiente información para calcular el área entre las curvas. \[ \begin{array}{l} y_{1}=12 x^{2}+48 x+2 \\ y_{2}=12 x^{3}+48 x^{2}+2 \end{array} \] \[ \begin{array}{l} \int_{a}^{b} y_{d}-2 answers -
\( \begin{array}{l}\text { Sea } f(x)=8 x \cos x \\ \text { Utiliza Integración por Partes para calcular: } \\ \int_{0}^{\pi} f(x) d x=F(\pi)-F(0) \\ F(\pi)=\pi+ \\ F(0)=\pi+ \\ \int_{0}^{\pi} f(x) d2 answers -
Utiliza el método de Integral Impropia. \[ \int_{4}^{\infty} f(x)=\frac{20}{x^{2}} \] Converge Diverge Si la integral converge, escribe el número a la cuál converge en Resultado. Si la integral div2 answers -
1. Compute \[ \int \frac{4 \sin ^{3}(x) \cos (x)+\sin ^{2}(x) \cos (x)+8 \sin (2 x)}{\sin ^{2}(x)+4} d x \]2 answers -
Utiliza el método de Integral Impropia. \[ \int_{0}^{\frac{\pi}{2}} f(x)=5 \tan x \] Converge Diverge Si la integral converge, escribe el número a la cuál converge en Resultado. Si la integral dive2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \) by implicit differentiation. \[ x^{2}+x y+y^{2}=9 \] \[ y^{\prime}= \]2 answers -
2 answers
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Utiliza la siguiente información para calcular el área entre las curvas. \[ \begin{array}{l} y_{1}=6 x^{2} \\ y_{2}=-12 x+144 \\ \int_{a}^{b} y_{c}-y_{d} d x \\ a=\quad, b= \\ c=\quad d= \\ \text {2 answers -
'ms' is + (plus) it is not variable
Completa los componentes para calcular con \( n \) particiones la Integral Definida: \[ \begin{array}{l} \int_{2}^{8} 4 x \operatorname{ms~} 3 d x \\ \triangle x=\quad / n \\ x_{i}=\quad i / n+ \\ f\l2 answers -
Utiliza el método de Integral Impropia. \[ \int_{0}^{\infty} f(x)=8 e^{-4 x} \] Converge Diverge Si la integral converge, escribe el número a la cuál converge en Resultado. Si la integral diverge,2 answers -
Ayuda
1. Consideremos la función \( z=f(x, y)=\ln (x y)+y^{2} \) y a las variables \( { }^{x} \), \( y \) definidas por \( x=e^{2 t}, y=e^{-2 t} \). a) Haga un diagrama de variables b) ¿Finalmente de cuá0 answers -
Determine the absolute maximum of \[ f(x, y)=x^{2}+y^{2}-x-y+2 \] on the unit disk \[ D=\left\{(x, y): x^{2}+y^{2} \leq 1\right\} \]2 answers -
2 answers
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choose which is true or false
\( \operatorname{Sea}\{(x, y): 2 \leq x \leq 3 ; 0 \leq y \leq x\} \) 1. La region es de tipo \( 1 y \) de tipo 2 2. La frontera de la region consiste en 4 segmentos y una curva que no es un segmento.2 answers -
2 answers
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2 answers
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ayuda
4. \( \mathrm{Si} w=x^{2}+y^{2}+z^{2} \) y a su vez \( x=\rho \operatorname{sen} \varphi \cos \theta, y=\rho \operatorname{sen} \varphi \operatorname{sen} \theta, z=\rho \cos \varphi \) \[ \begin{arra2 answers -
ayuda
2. Consideremos la función \( z=f(x, y)=e^{y / x} \) y a las variables \( { }^{x}, \quad y \) definidas por \( x=2 r \cos (t) \) \( y=4 r \operatorname{sen}(t) \). a) Haga un diagrama de variables. b0 answers -
ayuda
Consideremos la función \( z=f(x, y)=\ln (x y)+y^{2} \) y a las variables \( { }^{x}, y \) definidas por \( x=e^{2 t}, y=e^{-2 t} \). a) Haga un diagrama de variables b) ¿Finalmente de cuántas vari0 answers -
2 answers
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(1 point) Find an expression for the derivative of \( y \) at \( x=9 \), assuming that \( f(9)=-2 \) and \( f^{\prime}(9)=2 \) \[ y=\frac{1}{f(x)} \] \[ y^{\prime}(9)= \] \[ \begin{array}{l} y=\frac{f2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=3-z^{2}, \quad 0 \leq x, z \leq 5 ; \quad f(x, y, z)=z \] \( \iint_{\mathcal{S}} f(x, y, z) d S=\sqrt{\frac{25}{4} 5 \sqrt{101}+\log (5+\sqr2 answers -
Find \( \frac{d^{2} y}{d x^{2}} \) \( y=\frac{1}{x}+\tan x \) 1) \( -2 \sec ^{2} x \tan x+\frac{2}{x^{3}} \) 2) \( 2 \sec ^{2} x \tan x+\frac{2}{x^{3}} \) 3) \( -2 \sec ^{2} x \tan x-\frac{2}{x^{3}} \2 answers -
Thank you sm!! (:
Find \( y^{\prime \prime} \). \[ y=x^{\frac{6}{7}}+6 x \] \[ \mathrm{y}^{\prime \prime}= \]2 answers -
Thank you sm!! (:
Find \( y^{\prime \prime} \). \[ y=x^{\frac{6}{7}}+6 x \] \[ \mathrm{y}^{\prime \prime}= \]2 answers -
Let \( y=\left(2 e^{2}-x^{2}\right)(\ln x-8) \). \[ \frac{d y}{d x}= \] Let \( y=\frac{\sqrt[3]{x}}{7+3 \ln x} \) \[ \frac{d y}{d x}= \] Let \( y=\frac{1}{x^{7}-2 x^{2}-x} \) \[ g(x)=\sqrt{8 x-x^{4}+12 answers -
Thank you sm!! (:
Find \( y^{\prime \prime} \) \[ y=\frac{3 x+4}{2 x-1} \] \[ \mathrm{y}^{\prime \prime}= \]2 answers -
Differentiate the following functions. 5. \( y=\left(x^{3}+7 x-1\right)(5 x+2) \) 6. \( y=x^{-2}\left(4+3 x^{-3}\right) \) 7. \( y=\frac{2+x^{2}}{x+1} \)2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{r} y=\sqrt{\sin (x)} \\ y^{\prime}=\frac{\cos (x)}{2 \sqrt{\sin (x)}} \end{array} \]2 answers -
2 answers
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2 answers
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(1 point) Find an expression for the derivative of \( y \) at \( x=9 \), assuming that \( f(9)=-2 \) and \( f^{\prime}(9)=2 \). \[ \begin{array}{l} y=\frac{1}{f(x)} \\ y^{\prime}(9)= \end{array} \] \[2 answers