Calculus Archive: Questions from October 18, 2022
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20. \( \lim _{t \rightarrow-\infty} \frac{5-2 t^{3}}{t^{2}+1} \) 22. \( \lim _{x \rightarrow-\infty} \frac{x+4 x^{3}}{1-x^{2}+7 x^{3}} \) 24. \( \lim \sqrt[3]{\frac{3 s^{7}-4 s^{5}}{2 s^{7}+1}} \) 26.2 answers -
20. \( \lim _{t \rightarrow-\infty} \frac{5-2 t^{3}}{t^{2}+1} \) 22. \( \lim _{x \rightarrow-\infty} \frac{x+4 x^{3}}{1-x^{2}+7 x^{3}} \) 24. \( \lim _{s \rightarrow+\infty} \sqrt[3]{\frac{3 s^{7}-4 s2 answers -
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2. Integrar las siguientes expresiones. \( 5 \mathrm{pts} / \mathrm{cd} \) i. Integración por partes a. \( \int x^{11} \sin x^{4} d x \) b. \( \int x^{2} \sin 2 x d x \) ii. Integración por sustituc2 answers -
Integración por sustitución trigonométrica. a. \( \int \sqrt{4-x^{2}} d x \) b. \( \int \frac{\sqrt{25-16 x^{2}}}{x} d x \)2 answers -
2 answers
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Describe the domain and range of the function. \[ f(x, y)=\arccos (x+y) \] Domain: \[ \begin{array}{l} \{(x, y):-1 \leq y \leq 1\} \\ \{(x, y): x+y \leq-1\} \\ \{(x, y):-1 \leq x+y \leq 1\} \\ \{(x, y2 answers -
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Find all the first order partial derivatives for the following function. \( f(x, y)=\sin ^{2}\left(4 x y^{2}-y\right) \) \( f_{x}(x, y)=2 \sin \left(4 x y^{2}-y\right) \cos \left(4 x y^{2}-y\right) ;2 answers -
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Translation: Evaluate where C is represented by . "donde" = where
I. Evalúe \( \int_{c} F \cdot d r \) donde \( C \) está representada por \( r(t) \). a) \( F(x, y)=3 x i+4 y j ; C: r(t)=\cos (t) i+\operatorname{sen}(t) j \) donde \( 0 \leq t \leq \pi / 2 \) b) \(2 answers -
ts) Solve the initial-value problem I \( \quad y^{\prime \prime}+4 y^{\prime}+5 y=2 e^{-2 t} \sin t \quad y(0)=0, \quad y^{\prime}(0)=0 \)2 answers -
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Evaluate the integral using the Fundamental Theorem of the Line Integral a) soft curve from (0,0) to (3,8) b) soft curve frome (0, -π) to (3π/2, π/2)
II: Evalúe el integral utilizando el Teorema fundamental del integral de línea a) \( \int_{c}(3 y i+3 x j) \cdot d r \) C. curva suave desde \( (0,0) \) hasta \( (3,8) \) b) \( \int_{c} \cos (x) \op0 answers -
2 answers
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\( f_{x}(x, y, z)= \) \( f_{y}(x, y, z)= \) \( f_{z}(x, y, z)= \) (1 point) Let \( f(x, y, z)=\frac{x^{2}-4 y^{2}}{y^{2}+4 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z) \\ f_{y}(x, y, z)= \\ f_{2 answers -
\( f(x, y, z)=e^{x y z} ; \quad f_{x y z} \) \( f_{x y z}(x, y, z)=e^{x y z^{8}}\left(8 z^{7}+2 y x y z^{15}+8 x^{2} y^{2} z^{23}\right) \)2 answers -
28 and 30 please
\( \underline{23}, \underline{24}, \underline{25}, \underline{26}, \underline{27}, \underline{28}, \underline{29}, \underline{30} \), and \( \underline{31} \) Sketch the graph of the function. 23. \(2 answers -
\[ \frac{d y}{d x}+\frac{8}{x} y=4 x \quad y(2)=2 \] (As Bernoulle's) \[ \int \frac{f^{\prime}(x)}{f(x)} d x=\ln |f(x)|+c \]2 answers -
3 answers
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Calculate the double integral. \[ \iint_{R} x y e^{y} d A, R=\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq 1\} \]2 answers -
2. Let \( w=\left(x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}\right)^{k} \), where \( n \geq 2 \). Find all possible values for \( k \) such that \( \frac{\partial^{2} w}{\partial x_{1}^{2}}+\frac{\partial^{2 answers -
solve the ivp: y’ = (1+y^2)x ln x, y(1) = 1
Solve the IVP: \( y^{\prime}=\left(1+y^{2}\right) x \ln x, y(1)=1 \)2 answers -
help 👍🏼
Evaluate the function at the given values of the independent variables. Simplify the results. \[ f(x, y)=x \sin y \] (a) \( f\left(2, \frac{\pi}{4}\right) \) (b) \( f(5,4) \) (c) \( f(-2,0) \) (d) \(2 answers -
\[ f(x, y, z):=\frac{\sin \left(170 x^{2}+170 y^{2}+170 z^{2}\right)+76 x^{3}+59 y^{5}+26 z^{9}}{10 x^{2}+10 y^{2}+10 z^{2}} \] \( \lim _{(x, y, z) \rightarrow(0,0,0)} f(x, y, z)= \)1 answer -
\[ f(x, y, z):=\frac{\cos \left(120 x^{2}+120 y^{2}\right)-e^{40 x^{2}+40 y^{2}+12 x^{7} y^{4}}}{10 x^{2}+10 y^{2}}+z \cos (x) \] Find \( \lim _{(x, y, z) \rightarrow(0,0,5)} f(x, y, z)= \)2 answers -
Logarithmic Differentiation Differentiate each function wasing logarithmic differentiation. 1) \( y=\frac{x^{2}-3}{8 x^{3}-3 x} \) 2) \( y=4 x^{2} \) 3) \( y=\left(-5 x^{2}-7\right)\left(-3 x^{2}+5 x\2 answers -
Encontremos los valores extremos de \( f(x, y, z)=3 x-y-3 z \) sujeto a las siguientes restricciones \( g_{1}(x, y, z)=x+y-z=0 \) y \( g_{2}(x, y, z)=x^{2}+2 z^{2}-1=0 \) 1. La condicion (restriccion)0 answers -
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The question is in Spanish.
Encontrar los puntos que estan mas cercanos y lejanos del origen de la elipse, con \( 02 answers -
The question is in Spanish.
Encontremos los valores extremos de \( f(x, y, z)=3 x-y-3 z \) sujeto a las siguientes restricciones \( g_{1}(x, y, z)=x+y-z=0 \) y \( \quad g_{2}(x, y, z)=x^{2}+2 z^{2}-1=0 \) 1. La condicion (restri2 answers -
HELP PLEASE ASAP!! find y'
Find \( y^{\prime} \). a) \( y=\ln \left(3 x^{2}+1\right) \) b) \( y=e^{x} \tan x \)2 answers -
Problem 3. Solve the following IVP: \[ 2 x y-9 x^{2}+\left(2 y+x^{2}+1\right) \frac{d y}{d x}=0, \quad y(0)=-3 \] Problem 4. Solve the ODE: \[ (x+y) \sin y d x+(x \sin y+\cos y) d y=0 \]2 answers -
Solve the differential equation. a) \( y^{\prime \prime}+y^{\prime}=e^{x} \) b) \( y y^{\prime \prime}-\left(y^{\prime}\right)^{3}=0 \)2 answers -
2 answers
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If \( f(x)=3 x \sin (x) \cos (x) \), find \( f^{\prime}(x) \). \( f^{\prime}(x)= \) Find \( f^{\prime}(3) \). \( f^{\prime}(3)= \)2 answers -
En los problemas 23 y 24 , encuentre una función vectorial de la recta tangente a la curva dada en el punto correspondiente al valor que se indica de \( t \). 23. \( \mathbf{r}(t)=\langle\cos t \), s2 answers -
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Find \( y^{\prime} \) and \( y^{\prime \prime} \) by implicit differentiation. \[ \begin{array}{l} 5 x^{3}-3 y^{3}=5 \\ y^{\prime}=\frac{5 x^{2}}{3 y^{2}} \\ y^{\prime \prime}= \end{array} \]2 answers -
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\( \int(\sin x)^{3} \cdot \cos x d x \) \( \int \frac{1}{\sin x}+\frac{1}{x} \mathrm{dx} \) \( \int(\sin x)^{2} \cdot \tan x d x \) \( \int \sin x d x \)2 answers -
2 answers
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Find \( d y / d x \) by implicit differentiation. \[ y \sin \left(x^{2}\right)=-x \sin \left(y^{2}\right) \]2 answers -
show step by step the solution.
Encontrar la derivada de las siguientes expresiones. a. \( \frac{1}{2} \ln \sin x \) b. \( g(x)=\log _{x^{3}} \frac{(2 x-1)^{2}}{(x+3)^{3}} \) c. \( \frac{d}{d x} \cos ^{-1}(2 x) \) d. \( \frac{d}{d x2 answers -
2 answers
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2 answers
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Find the partial derivatives of the function \[ \begin{array}{l} f(x, y)=\int_{y}^{x} \cos \left(4-\left(t^{2}+8 t\right)\right) d t \\ f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \]2 answers -
number 25 only
In Exercises 9-26, calculate the derivative with respect to \( x \). 9. \( 3 y^{3}+x^{2}=5 \) 10. \( y^{4}-2 y=4 x^{3}+x \) 11. \( x^{2} y+2 x^{3} y=x+y \) 12. \( x y^{2}+x^{2} y^{5}-x^{3}=3 \) 13. \(2 answers -
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Problem 2. Solve the following IVP i) \( \frac{d y}{d x}+\mathbf{1} y=e^{x}, \quad y(0)=\frac{1}{2} \) ii) \( \frac{d y}{d x}+\frac{y}{x}=x, \quad y(0)=1 \)1 answer -
Evaluate \( \iiint_{E} 3 x z d V \) where \( E=\{(x, y, z) \mid 1 \leq x \leq 2, x \leq y \leq 2 x, 02 answers