Calculus Archive: Questions from February 20, 2023
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3 answers
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44. \( \int_{2}^{6} \frac{y}{\sqrt{y-2}} d y \) 46. \( \int_{0}^{1} \frac{1}{2-3 x} d x \) 48. \( \int_{-1}^{1} \frac{d x}{x^{2}-2 x} \)2 answers -
2 answers
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Find the solution of the IVP \[ y^{\prime \prime}-4 y^{\prime}+4 y=2, \quad y(0)=2, \quad y^{\prime}(0)=-2 \]2 answers -
2. Find and describe the domain and range of the following functions: (a) \( f(x, y)=\sqrt{4-x^{2}-y^{2}} \), (b) \( f(x, y)=\frac{3}{\sqrt{25-x^{2}-y^{2}}} \), (c) \( f(x, y, z)=\frac{\sqrt{x+y}}{x z2 answers -
det
Determine \( f_{x x} f_{y y}-\left(f_{x y}\right)^{2} \) when \[ f(x, y)=\frac{2}{3} x^{3}+2 y^{2}+9 x+4 y+9 x y . \] 1. \( f_{x x} f_{y y}-\left(f_{x y}\right)^{2}=8 x+81 \) 2. \( f_{x x} f_{y y}-\le2 answers -
Solve the following Bernoulli IVP. Show your work. \[ \begin{array}{c} y^{\prime}+y=x y^{2} \\ y(0)=3 \end{array} \]2 answers -
\( \int \frac{10 d x}{(x+1)\left(x^{2}+4\right)}= \) \( \int \frac{4 \sin (\theta)}{\cos ^{3}(\theta)+7 \cos (\theta)} d \theta= \)2 answers -
2 answers
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Solve the given initial-value problem. \[ y^{\prime \prime}+y^{\prime}+4 y=0, \quad y(0)=y^{\prime}(0)=0 \] \[ y(x)= \]2 answers -
Question 7 \[ \begin{array}{l} f=e^{x} \cdot \sin y \cdot \ln z \\ \frac{\vartheta f}{\vartheta z}= \end{array} \] \( e^{x} \cdot \sin y \cdot \ln z \) \( e^{x} \cdot \cos y \cdot \ln z \) \( e^{x} \c2 answers -
2 answers
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Comparar integrales 70) Considere la integral \( y=\frac{1}{\sqrt{6 x-x^{2}}} d x \) a) Halle la integral al completar el cuadrado b) Halle la integral al hacer la sustituciĆ³n \( u=\sqrt{x} \) Determ2 answers -
Encuentre la integral definida 32) \( \int_{0}^{\frac{1}{\sqrt{2}}} \frac{\cos ^{-1} x}{\sqrt{1-x^{2}}} d x \) Encuentre la integral indefinida completando el cuadrado 38) \( \int \frac{2}{\sqrt{-x^{22 answers -
(1 point) Let \( f(x, y, z)=\frac{x^{2}-2 y^{2}}{y^{2}+4 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
Need assistance with this please
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=e^{4 e^{x}} \] \[ y^{\prime}= \]2 answers -
please solve a and L
1. Find the following derivatives: (a) \( f(x)=x^{2} \sin x \) (g) \( f(\theta)=\theta \cos \theta \sin \theta \) (b) \( f(x)=e^{x} \cos x \) (h) \( f(x)=x \cos x+2 \tan x \) (c) \( y=\sec \theta \tan2 answers -
help
Determine if the functions below are implicit or explicit functions. (Write your answers as A-Explicit, etc.) A. \( \cos \left(\frac{x}{y}\right)=x+y \) C. \( y=x^{3}+2 \) B. \( y=x \sin (x) \) D. \(2 answers -
need last 2 please asap
For the given parametric equations, find the points \( (x, y) \) corresponding to the parameter values \( t=-2,-1,0,1,2 \). \[ x=\ln \left(4 t^{2}+1\right), \quad y=\frac{t}{t+7} \] \[ t=-2 \quad(x, y2 answers -
29. \( y^{\prime}=\sin y, y(0)=-\pi / 6, y(0)=\pi / 6, y(0)=7 \pi / 4 \) 30. \( y^{\prime}=1+\sin y, y(0)=0, y(0)=\pi \)0 answers -
2 answers
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Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For Part of the surface \( x=z^{3} \), where \( 0 \leq x, y \leq 4^{-\frac{y}{2}} ; \quad f(x, y, z)=x \) \[ \iint_{S} f(x, y, z) d S= \]2 answers -
Let \( f(x, y)=\left\{\begin{array}{ll}\frac{x^{2}-16 y^{2}}{x-4 y} & (x, y) \neq(4,1) \\ 1 & (x, y)=(4,1)\end{array}\right. \) 1. Find the limit \( \lim _{(x, y) \rightarrow(4,1)} f(x, y) \) 2. Is \(2 answers -
Need #40 a) and b)
Continuity for Three Variables At what points \( (x, y, z) \) in space are the functions in Exercises 35-40 continuous? 35. a. \( f(x, y, z)=x^{2}+y^{2}-2 z^{2} \) b. \( f(x, y, z)=\sqrt{x^{2}+y^{2}-12 answers -
2 answers
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Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ x^{2}+y^{2}=25, \quad 0 \leq z \leq 7 ; \quad f(x, y, z)=e^{-z} \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
1. Compute the derivative of the following functions. a. \( y=\sqrt{e^{5 x}+3 x^{4}} \) b. \( y=2^{\sin (3 x)} \) c. \( y=\ln \left(\cos ^{-1}\left(x^{3}\right)\right) \) d. \( y=\log \left(x^{2} \sqr2 answers