Calculus Archive: Questions from March 03, 2023
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Complete the identity. \[ \frac{\sin \theta}{1+\sin \theta}-\frac{\sin \theta}{1-\sin \theta}=? \] A. \( -2 \tan ^{2} \theta \) B. \( \sin \theta \tan \theta \) C. \( \sec \theta \csc \theta \) D. \(2 answers -
Find the slope in the \( x \)-direction at the point \( P(0,2, f(0,2)) \) on the graph of \( f \) when \[ f(x, y)=4\left(y^{2}-x^{2}\right) \ln (x+y) . \] 1. slope \( =2 \) 2. slope \( =4 \) 3. slope2 answers -
Let f(x,y,z)=x2−6y2y2+4z2 . Then fx(x,y,z) = fy(x,y,z) = fz(x,y,z) =
(1 point) Let \( f(x, y, z)=\frac{x^{2}-6 y^{2}}{y^{2}+4 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
\[ f(x, y, z)=\left[5 \cdot \sin (x \cdot y \cdot z)-5 \cdot x \cdot y \cdot z, 2 \cdot y^{2} \cdot \cos (z),-e^{x^{2} \cdot y-4 \cdot z}\right] \] find the Jacobian matrix Df. \[ D f= \] Evaluate \(2 answers -
\[ \text { ind } \int_{1}^{e} \int_{1}^{e}\left(x \cdot \frac{\ln (y)}{\sqrt{y}}+y \cdot \frac{\ln (x)}{\sqrt{x}}\right) d y d x \] SolidUnderSurface \( z=x^{\star} \ln (y) / y+y^{\star} \ln (x) / x \2 answers -
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1.- Encuentre el plano tangente a el paraboloide eliptico \( f(x, y)=2 x^{2}+y^{2} \) en el punto \( (1,1,3) \) 2.- Encuentre el plano tangente a el paraboloide hiperbólico \( f(x, y)=3 y^{2}-2 x^{2}2 answers -
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( 1 point) Find \( y \) as a function of \( x \) if \[ y^{(4)}-8 y^{\prime \prime \prime}+16 y^{\prime \prime}=0 \] \[ y(0)=2, \quad y^{\prime}(0)=12, \quad y^{\prime \prime}(0)=16, \quad y^{\prime \p2 answers -
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Differentiate. \[ y=\frac{3 x-5}{2 x^{2}+1} \] A. \( \frac{-6 x^{2}+17 x+8}{\left(2 x^{2}+1\right)^{2}} \) B. \( \frac{-6 x^{2}+20 x+3}{\left(2 x^{2}+1\right)^{2}} \) c. \( \frac{18 x^{2}-20 x+3}{\lef2 answers -
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Find \( y^{\prime \prime} \) if implicit differentiation produces the following equation in \( y^{\prime} \) : \[ y^{\prime} \cdot \tan \left(\sqrt[3]{x^{2}+5}\right)=\csc ^{5}\left(y^{3}\right)-e^{52 answers -
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\[ \text { If } y^{\prime \prime}=\frac{1}{(x+1)^{2}}, y(0)=2, y^{\prime}(0)=1 \text { then } y^{\prime}= \] and \( y= \)2 answers -
2. Suppose that \( z=\sin x \cos 2 y \) where \( x=u^{2}+v \) and \( y=u v \). Find \( \frac{\partial z}{\partial u} \).2 answers -
Question 9 If \( y^{\prime \prime}=\frac{1}{(x+1)^{2}}, y(0)=2, y^{\prime}(0)=1^{\text {then }} y^{\prime}= \) and \( y= \)2 answers -
If \( y^{\prime \prime}=\frac{1}{(x+1)^{2}} \cdot y(0)=2 \cdot y^{\prime}(0)=1^{\text {then }} y^{\prime}=\quad \) and \( y= \)2 answers -
Pls assist me?
\( \begin{array}{l}\text { ind } \frac{d^{2} y}{d x^{2}} \\ y=-2 x^{9}-1\end{array} \) \( \frac{d^{2} y}{d x^{2}}= \)2 answers -
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Find the limit. \[ \lim _{(x, y) \rightarrow(0,0)} \frac{5 x^{2}+10 y^{2}+2}{5 x^{2}-10 y^{2}+9} \] 1 \( -1 \) \( \frac{2}{9} \) No limit2 answers -
Find y'
(d) \( \sqrt{x y}=1+x^{2} y \quad \) Answer: \( y^{\prime}=\frac{4 x y \sqrt{x y}-y}{x-2 x^{2} \sqrt{x y}} \) (e) \( y \sin x^{2}=x \sin y^{2} \quad \) Answer: \( y^{\prime}=\frac{2 x y \cos x^{2}-\si2 answers -
Please show all steps. Thank You!!!
Find all the second partial derivatives. \[ \begin{array}{l} \quad f(x, y)=x^{5} y^{5}+3 x^{7} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
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11.C5 Un rociador de jardín oscilunte descarga agua con una velocidad inicial \( v_{a} \) de \( 10 \mathrm{~m} / \mathrm{s} \). a) Si se sabe que los lados del quioseo BCDE son abiertos. pero no asi2 answers -
Evaluate the integral. \[ \int_{-5}^{5} f(x) d x \text { where } f(x)=\left\{\begin{array}{ll} 5 & \text { if }-5 \leq x \leq 0 \\ 25-x^{2} & \text { if } 02 answers -
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1. Evaluate: 2. \( \sin \alpha=-\frac{4}{5}, \alpha \in \mathbb{I} \) a. \( \sin 195^{\circ} \) \( \tan \beta=2, \beta \in I \). b. \( \tan 105^{\circ} \) Find a. \( \sin (\alpha+\beta) \) c. \( \cos2 answers -
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Current Attempt in Progress Solve the initial value problem \[ y^{\prime \prime}+4 y^{\prime}+5 y=0, y(0)=1, y^{\prime}(0)=0 \] \[ \begin{array}{l} y=\cos t+2 \sin t \\ y=2 e^{-2 t} \cos t+e^{-2 t} \s2 answers -
(1 point) If \( 4 \sin x+9 \cos y=\sin x \cos y \), find \( d y / d x \) by implicit differentiation. \[ d y / d x= \]2 answers -
Find the quadratic approximation to \[ f(x, y)=\sqrt{1+4 x-2 y} \] at \( P(0,0) \). 1. \( Q(x, y)=1+2 x-y-2 x^{2}-2 x y-\frac{1}{2} y^{2} \) 2. \( Q(x, y)=1-2 x+y+2 x^{2}-2 x y-y^{2} \) 3. \( Q(x, y)=2 answers -
Find the Quadratic Approximation to Find the quadratic approximation to \( f(x, y) \) at \( P(0,0) \) when \( f(0,0)=1 \) \[ f(x, y)=e^{-x+2 y^{2}} \] \[ f_{x}(0,0)=-2, \quad f_{y}(0,0)=0, \] at \( P(2 answers -
Given \( f(x, y)=2 x^{3}+4 x^{2} y^{4}-5 y^{6} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] Question Help: Video2 answers -
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\( y=x^{3}-3\left(x^{2}+\pi^{2}\right) \) \( y=(x+1)^{2}\left(x^{2}+2 x\right) \) \( S=\frac{\sqrt{t}}{1+\sqrt{t}} \) \( y=\left(\frac{2 \sqrt{x}}{2 \sqrt{x}+1}\right)^{2} \) \( y=4 x \sqrt{x+\sqrt{x}2 answers -
find the quadratic app
Find the Quadratic Approximation to \( f(x, y) \) at \( P(0,0) \) when \( f(0,0)=1 \) \[ f_{x}(0,0)=-2, \quad f_{y}(0,0)=0, \] and \[ f_{x x}(0,0)=0, f_{x y}(0,0)=-3, f_{y y}(0,0)=1 . \] 1. \( Q(x, y)2 answers -
Find the quadratic approximation to \[ f(x, y)=e^{-x+2 y^{2}} \] at \( P(0,0) \). 1. \( Q(x, y)=1-2 x+\frac{1}{2} x^{2}-2 y^{2} \) 2. \( Q(x, y)=1-x+\frac{1}{2} x^{2}-2 y^{2} \) 3. \( Q(x, y)=1-x+\fra2 answers -
\[ \begin{array}{l} a_{1}-1.2 a_{0}=-300 \\ 2 a_{2}-1.2 a_{1}=0 \\ 3 a_{3}-1.2 a_{2}=0 \\ 4 a_{4}-1.2 a_{3}=0 \end{array} \] Solve for the coefficients \( a_{1^{\prime}} a_{2^{\prime}} a_{3^{\prime}}2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{l} \quad y=e^{\alpha x} \sin \beta x \\ y^{\prime}= \\ y^{\prime \prime}= \end{array} \]2 answers -
Choose the expression equal to \( \frac{d y}{d x} \) if \[ \tan (x+y)=x \] (Use implicit differentiation.) \[ \begin{array}{l} \tan ^{2}(x+y) \\ \sec ^{2}(x+y) \\ \ln (\sec (x+y)) \\ \sin ^{2}(x+y)-12 answers -
Solve the initial value problem: \[ \begin{array}{l} \frac{d^{4} y}{d x^{4}}=y^{(4)}(x)=-\cos x+8 \sin 2 x \\ y^{\prime \prime \prime}(0)=0, y^{\prime \prime}(0)=y(0)=1, y(0)=3 \end{array} \]2 answers -
#12 please show your work
Derivative Calculations In Exereises 1-8, given \( y=f(a) \) and \( y=g(x) \). find \( d y / d r= \) \( d y / d x=f^{\prime}(s(x)) g^{\prime}(x) \) 1. \( y=6 u-9, \quad u=(1 / 2) x^{4} \quad \) 2. \(2 answers