Calculus Archive: Questions from October 16, 2022
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Drag the answers (Laplance)
1. \( L\left\{e^{-7 t}\right\}= \) 2. \( L\{\sin 2 t\}= \) \( \frac{\frac{1}{2}}{s^{2}-\frac{1}{4}} \quad \frac{120}{s^{6}} \) \( \frac{2}{s^{2}+4} \) 3. \( L\left\{t^{5}\right\}= \) 4. \( L\{\cos \sq2 answers -
2 answers
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Find the partial derivatives of the function \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \end{array} \] \[ f(x, y)=x y e^{7 y} \]2 answers -
2 answers
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12. \( y=(\arcsin 2 x)^{2} \) 17. \( y=\sqrt{\arctan x} \) 31. \( y=x \tan ^{-1}(4 x) \) 42. \( y=\ln \left(\arcsin x^{2}\right) \)2 answers -
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Calculate y'
\( y=\sqrt{\arctan x} \) \( y=x \tan ^{-1}(4 x) \) \( y=\ln \left(\arcsin x^{2}\right) \)2 answers -
2 answers
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SCALCET8 3.2.011.MI. Differentiate. \[ F(y)=\left(\frac{1}{y^{2}}-\frac{7}{y^{4}}\right)\left(y+5 y^{3}\right) \]2 answers -
SCALCET9 3.5.039.EP. Find \( y^{\prime} \) and \( y^{\prime \prime} \) by implicit differentiation. Simplify where possible. \[ x^{2}+6 y^{2}=6 \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]2 answers -
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Solve the following \( D E \) problems. (1) \( y^{\prime \prime}+4 y=-10 \sin (2 t) \). (2) \( y^{\prime \prime}-2 y^{\prime}+y=2 e^{t} ; \quad y(0)=y^{\prime}(0)=1 \).2 answers -
1) Classify by name the following surfaces 2) Draw the level curves for f(x,y)=¼x^2+ ¼y^2 +1 3) Evaluate the following limits 4) Prove using trajectories that the following limits does not exist 5)
6) Halla la ecuación del plano tangente \( a z=(x+1)^{2}-2(y-2)^{2}-3 \) en el punto \( (2,3,4) \) \( (10 \mathrm{pts} \). 7) Halla la linearizacion de \( f(x, y)=1+x \ln (x y-5) \) en el punto \( (22 answers -
Thank you, please show steps.
5) Find the parcial derivate indicated a) For \( f(x, y)=x \sin (x y) \) Find \( f_{x}(x, y) y f_{y}(x, y)(6 \) pts. \( ) \) \( f_{x}(x, y)=f_{y}(x, y)= \) b) For \( f(x, y, z)=4 x y^{2} z+3 x^{2} z y2 answers -
5) Halla las derivadas parciales indicadas a) Para \( f(x, y)=x \sin (x y) \) halla \( f_{x}(x, y) \quad y f_{y}(x, y)(6 \) pts.) \( f_{x}(x, y)= \) \( f_{y}(x, y)= \) b) Para \( f(x, y, z)=4 x y^{2}2 answers -
4) Prueba usando trayectorias que el siguiente límite no existe \[ \lim _{(x, y) \rightarrow(0,0)} \frac{3 x y}{x^{2}+4 y^{2}} \quad(6 \text { pts. }) \] 5) Halla las derivadas parciales indicadas a)2 answers -
6) Halla la ecuación del plano tangente a \( z=(x+1)^{2}-2(y-2)^{2}-3 \) en el punto \( (2,3,4) \) \( (10 \) pts. \( ) \) 7) Halla la linearizacion de \( f(x, y)=1+x \ln (x y-5) \) en el punto (2,3)0 answers -
10) Sea \( f\left(x, y 0=x^{3}-3 x+3 x y^{2}\right. \) a) Halla sus 4 puntos críticos ( 5 pts.) b) Halla cuales son máximos, mínimos o punto silla. (5 pts.) 11) Halla 3 números positivos que sumen2 answers -
3) Evaluate the following limits 4) Prove using trajectories that the following limit does not exist
3) Evalúa los siguientes límites a) \( \lim _{(x, y) \rightarrow(2,2)} \frac{x^{4}-4 y^{2}}{x^{3}-2 x y}(5 \mathrm{pts} \). b) \( \lim _{(x, y) \rightarrow(4,4)} \frac{\sqrt{x}-\sqrt{y}}{x^{2}-y^{2}2 answers -
a) Para \( f(x, y)=x \sin (x y) \) halla \( f_{x}(x, y) y f_{y}(x, y)(6 \) pts.) \( f_{x}(x, y)= \) \[ f_{y}(x, y)= \] b) Para \( f(x, y, z)=4 x y^{2} z+3 x^{2} z y+5 x y z^{2} \) Halla \( f_{x y z y2 answers -
8) Halla la derivada direccional de \( f(x, y, z)=x y^{2} \tan ^{-1} z \) en el punto \( (2,1,1) \) en la dirección del vector \( (10 \mathrm{pts} \).) \[ u=i+j+k \] 9) Sea \( f(x, y)=3 x^{2} y+2 x y0 answers -
Help Entering Answers (1 point) Find the gradient vector field of the following functions: \[ \begin{array}{ll} f(x, y, z)=7 \tan (-x-y z), & \nabla f(x, y, z)= \\ g(x, y, z)=6 x \ln \left(3 z+y^{3}\r2 answers -
2 answers
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If \( y^{\prime}=\sin (8 t) \), then \( y= \) If \( y^{\prime}=\cos \left(\frac{t}{8}\right) \), then \( y= \) If \( y^{\prime}=\sin (8 t)+\cos \left(\frac{t}{8}\right) \), then \( y= \)2 answers -
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(1 point) Find \( y \) as a function of \( t \) if \[ 36 y^{\prime \prime}+12 y^{\prime}+y=0 \] \[ y\left(0^{\prime}-2 \quad \sqrt{\prime}(n)-8\right. \]2 answers -
2 answers
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2) Draw the level curves for 𝑓(𝑥, 𝑦) = 1 4 𝑥 2 + 1 4 𝑦 2 + 1 for the following values a) 𝑘 = 2 (3 pts.) b) 𝑘 = 1 (3 pts.) c) 𝑘 = 0 (3 pts.)
2) Dibuja las curvas de nivel para \( f(x, y)=\frac{1}{4} x^{2}+\frac{1}{4} y^{2}+1 \) para los siguientes valores a) \( k=2 \) (3 pts. \( ) \) b) \( k=1 \) (3 pts.) c) \( k=0 \) (3 pts.)2 answers -
please help!!
Help Entering Answers (1 point) Find the gradient vector field of the following functions: \[ f(x, y)=x \ln \left(1+y^{2}\right), \quad \nabla f(x, y)= \] \[ g(x, y)=2 \tan (-2 x-y), \quad \nabla g(x,2 answers -
4) Prove using trajectories that the following limit does not exist lim (𝑥,𝑦)→(0,0) 3𝑥𝑦 𝑥 2+4𝑦2 (6 points)
4) Prueba usando trayectorias que el siguiente límite no existe \[ \lim _{(x, y) \rightarrow(0,0)} \frac{3 x y}{x^{2}+4 y^{2}} \quad(6 \text { pts. }) \]0 answers -
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11) Find 3 positive numbers that add up to 12 and that the sum of their squares is a value minimum. (10 points)
11) Halla 3 números positivos que sumen 12 y que la suma de sus cuadrados sea un valor minimo. \( (10 \) pts. \( ) \)2 answers -
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2) Dibuja las curvas de nivel para \( f(x, y)=\frac{1}{4} x^{2}+\frac{1}{4} y^{2}+1 \) para los siguientes valores a) \( k=2 \) (3 pts. \( ) \) b) \( k=1 \) (3 pts. \( ) \) c) \( k=0 \quad(3 \) pts. \0 answers -
6) Halla la ecuación del plano tangente a \( z=(x+1)^{2}-2(y-2)^{2}-3 \) en el punto \( (2,3,4) \) \( (10 \) pts. \( ) \) 7) Halla la linearizacion de \( f(x, y)=1+x \ln (x y-5) \) en el punto (2,3)2 answers -
draw a curve of level for f(x,y) = 1/4x^2 + 1/4y^2 + 1 follow values:
2) Dibuja las curvas de nivel para \( f(x, y)=\frac{1}{4} x^{2}+\frac{1}{4} y^{2}+1 \) para los siguientes valores a) \( k=2(3 \) pts. \( ) \) b) \( k=1 \) (3 pts. \( ) \) c) \( k=0 \quad(3 \) pts. \(0 answers -
2 answers
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Solve the following boundary-value problem: \( y "+9 y=0, ; y(0)=-1, y\left(\frac{\pi}{6}\right)=1 \) \[ y=\cos 3 x+\sin 3 x \] B \( y=-\cos 3 x+\sin 3 x \) C. \( y=\cos 3 x-\sin 3 x \) D) \( y=-\cos0 answers -
2. Compute \( \iint_{\mathcal{R}} x d \Lambda \), where \( \mathcal{R}=\left\{(x, y): x \geq 0, y \geq 0,1 \leq x^{2}+y^{2} \leq 4\right\} \).2 answers -
6. Find the equation of the plane tangent to 𝑧 = (𝑥 + 1)^2 − 2(𝑦 − 2)^2 − 3 at the point (2, 3, 4) 7. Find the linearization of f(x,y) = 1 + xIn(xy - 5) at the point (2,3)
6) Halla la ecuación del plano tangente a \( z=(x+1)^{2}-2(y-2)^{2}-3 \) en el punto \( (2,3,4) \) \( (10 \) pts.) 7) Halla la linearizacion de \( f(x, y)=1+x \ln (x y-5) \) en el punto (2,3) (10 pts2 answers -
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urgent
Find \( d y / d x \) by implicit differentiation. \[ \sin x+\cos y=\sin x \cos y \] \[ d y / d x= \]2 answers -
2 answers
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Answer all three please.
\( f(x)=5 \sin x-\cos x \) \( g(x)=\cos x \cdot e^{x} \) \( h(x)=\frac{\sin x+\cos x}{\sin x} \)2 answers -
2 answers