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Calculus Archive: Questions from March 28, 2023

• Use Lagrange Multiplier Show all steps Correct Answer is: Max:3/2 Min: 1/2
  17-20 Find the extreme values of \( f \) subject to both constraints. 17. \( f(x, y, z)=x+y+z ; \quad x^{2}+z^{2}=2, \quad x+y=1 \) 18. \( f(x, y, z)=z ; \quad x^{2}+y^{2}=z^{2}, \quad x+y+z=24 \) 19.
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  I. Considere \( x^{2} y-4 x=5 \) para hallar su segunda derivada de \( \mathrm{y} \) con respecto a \( \mathrm{x} \), simplifique para dejarla expresada en términos de las variable \( x \& \) y. II.
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  8. Solve \( \quad y^{\prime}+2 y^{2} y^{\prime}=y \cos x ; y(0)=1 \).
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• Lagrange optimization
  Ejercicio Optimización Langrange \[ \begin{array}{l} F(x), \quad g(x)=0 \\ F(x, y, d)=f(x, y)-d_{g}(x) \\ \left.\begin{array}{l} F x=0 \\ F y=0 \\ F y=0 \end{array}\right\} P(x, y, d) \Rightarrow f(x
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  Excuentirn \( y^{\prime} \) 1) \( e^{-x} \sec ^{-1} e^{-x} \) \( R=\frac{-e^{-x}}{\sqrt{e^{-2 x}-1}}-e^{-x} \sec ^{-1} e^{-x} \)
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  II Encuentin la integincion \[ \text { 3) } \int \frac{\operatorname{sen} x}{\cos ^{2} x+1} d x \quad R=-\tan ^{-1}(\cos x)+c \]
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  c) \( y=\left(x^{3}+1\right) z^{x^{2}+1} \) Anwer: d) \( y=\log _{3} 2 x+1 \)
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• Solve this way
  3. \( \int \frac{4-7 x}{1+x^{2}} d x \) \( \begin{array}{l}\text { 3. } \int \frac{8-3 x}{\sqrt{1-x^{2}}} d x \\ \int \frac{8-3 x}{\sqrt{1-x^{2}}} d x=\int \frac{8}{\sqrt{1-x^{2}}}-3 x\left(1-x^{2}\r
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  Find \( d y / d x \) by implicit differentiation. (a) \( x^{3}-x y^{2}+y^{3}=1 \) (b) \( \cos (x y)=1+\sin y \) (c) \( x \sin y+y \sin x=1 \) (d) \( \tan (x-y)=\frac{y}{1+x^{2}} \)
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  [-/1 Points] LARCALC12 2.4.003. Complete the table. [-/1 Points] Complete the table.
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• Please show work. Thank you
  tiate. Find \( y^{\prime} \) for \( y=\frac{x^{2}}{9-4 x} \) \[ y^{\prime}=\frac{9 x}{(9-4 x)^{2}} \] \[ y^{\prime}=\frac{-12 x^{2}+18 x}{(9-4 x)^{2}} \] \[ y^{\prime}=\frac{-4 x^{2}+18 x}{(9-4 x)^{2}
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  Find all the complex roots. Write the answer in the indicated form. The complex square roots of \( 16\left(\cos 210^{\circ}+i \sin 210^{\circ}\right) \) (polar form) \( 4\left(\cos 105^{\circ}+i \sin
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• question 46 thank you!
  Use the product or quotient rule or the generalized power rule to find the derivative of each of the given functions. (See Examples 8-10.) 35. \( y=(x+1)(x-3)^{2} \) 36. \( y=(2 x+1)^{3}(x-5) \) 37. \
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  (1 point) Calculate all four second-order partial derivatives of \( f(x, y)=2 x^{2} y+7 x y^{3} \). \[ f_{x x}(x, \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]
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  What is the expression for the slope of the graph \( (x-5)^{2}+(y+1)^{2}=4 \) at any point \( (x, y) \) ? a. \( y^{\prime}=\frac{x-5}{y+1} \) b. \( y^{\prime}=-\frac{x+5}{y-1} \) \( y^{\prime}=-\frac{
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• Please show all the work
  9. Given that \( U(2)=3, U^{\prime}(2)=-4, V(2)=1 \) and \( V^{\prime}(2)=5 \), find \( y^{\prime}(2) \) if (a). \( y=U V \) (b). \( y=\frac{U}{V} \) (c). \( y=x^{2} U+3 V \)
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• Please show all the work
  15. For each of the following, find \( \frac{d y}{d x} \) : (a). \( y=(\sec x+\tan x)(\sec x-\tan x) \) (b). \( y=\frac{4 x e^{x}}{x^{2}+1} \) (c). \( y=x^{2} \cos x-2 x \sin x-2 \cos x \) (d). \( y=e
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  Find all local extrema of \( f(x, y)=x^{2}-6 x+y^{2}-4 y+12 \)
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• I would like the know the procedures of this exercise please, i appreciate it.
  Tres alelos (otras versiones de un gen), \( A, B \) y \( O \) determinan los cuatro tipos de sangre a saber, \( A(A A o A O), B(B B o B O), O(O O) \) y \( A B \). La ley de HardyWeinberg establece que
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  Find \( d y / d x \). \[ \begin{array}{c} x=\sqrt[4]{t} \\ y=6-t \\ \frac{d y}{d x}=\frac{\sqrt[4]{t^{3}}(6-t)}{t} \end{array} \]
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• Find y^1
  \( \begin{array}{l}e^{-x} \sec ^{-1} e^{-x} \quad \text { prucedian } \quad \text { parade }=\text { dado } \\ R=\frac{-e^{-x}}{\sqrt{e^{-2 x}-1}}-e^{-x} \sec ^{-1} e^{-x} \\ \text { 2) } \sec ^{-1} \
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  2. (10 points) Find \( d w / d t \) for \( w=x e^{y}+y \sin x-\cos z \) if \( x=2 t^{2}, y=t-1 \), and \( z=\pi t \).
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  34. Astroide. Encuentre la longitud total de la gráfica de la astroide \( x^{2 / a}+y^{2 / 3}=4 \).
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  37. Encontrar el área de una superficies de revolución. Configure y evalúe la integral definida para el área de la superficie generada al rotar la curva alrededor del eje \( x \). \[ y=\frac{1}{3}
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  Find \( y^{\prime} \). \[ y=\log _{8}\left(x^{4}-4 x^{3}+1\right) \] \[ y^{\prime}= \] /9.09 Points] Find \( y^{\prime} \). \[ y=(\ln (x))^{8} \] \[ y^{\prime}= \]
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  Find the limit. \[ \lim _{(x, y) \longrightarrow(0,1)} \frac{y^{5} \sin x}{x} \] 1 0 \( \infty \) No Limit
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  Evaluate the triple integral over the bounded region \( E=\left\{(x, y, z) \mid g_{1}(y) \leq x \leq g_{2}(y), c \leq y \leq d, u_{1}(x, y) \leq z \leq u_{2}(x, y)\right\} \). \[ \iiint_{E}(x+y) d V \
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  Evaluate the integral. \[ \int \frac{6+x}{\sqrt{36-x^{2}}} d x \] A) \( 6 \tan ^{-1} \frac{x}{6}-\sqrt{36-x^{2}}+C \) B) \( \sin ^{-1} \frac{x}{36}-2 \sqrt{36-x^{2}}+C \) C) \( \frac{1}{6} \tan ^{-1}
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• Find all possible values of y if ((1)/(6),y) lies on the unit circle.
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• evaluate the partial derivatives of each function at the given point.
  2. Evaluar las derivadas parciales de cada función en el punto dado: a. \( f(x, y)=\frac{x y}{x-y} \) en el punto \( (2,-2) \). b. \( g(x, y)=\frac{6 x y}{\sqrt{4 x^{2}+5 y^{2}}} \) en el punto \( (1
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• Find (if possible ) the rational zeros of the fun C(x)=2x^(3)+3x^(2)-1 x=-1,1, - (1)/(2),(1)/(2)
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• Verify: (sin^(3)x+cos^(3)x)/(sinx+secx)=1-sinx*cosx
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• For each function, find the values ​​of x and y.
  4. Para cada función hallar los valores de \( x \) y los de \( y \) tales que \( \frac{\partial f}{\partial x}(x, y)=0 \) y \( \frac{\partial f}{\partial y}(x, y)=0 \) a. \( f(x, y)=x^{2}+4 x y+y^{2}
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• consider the function w
  6. Considere la función \( W=f(x, y) \), donde \( x=u-v, \quad y=v-u \). Verificar que \( \frac{\partial W}{\partial u}+\frac{\partial W}{\partial v}=0 \).
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  \( y=4 \sin ^{3}(3 x+1) \) \( y=\frac{2-x}{3 x+1} \)
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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 x+y \leq 1\} \\ \{(x, y):-1 \leq y \leq 1\} \\ \{(x, y): x+y \geq 1\} \\ \{(x, y
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  Evaluate the integral. \[ \int_{0}^{\pi / 4} \sin ^{2}(2 \theta) d \theta \]
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• {(ln3.32)/(ln10)} aplify your answer. Use integers or decir
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• strar la identidad. (sinx)/(1+cosx)+(1+cosx)/(sinx)=2cscx
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  3. Hallar \( \frac{\partial}{\partial x}\left(\frac{\partial f}{\partial x}\right)=\frac{\partial^{2} f}{\partial x^{2}}, \quad \frac{\partial}{\partial y}\left(\frac{\partial f}{\partial y}\right)=\f
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• mostrar la identidad. (1-sin^(2)x)cscx=cosxcotx
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• f(x)=4x^(3)-21x^(2)+21x-4 necessary, to identify the octuol zer
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• Donations aun Lar Wash Proceeds 23w+85 17w+112
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  4. Para cada función hallar los valores de \( x \) y los de \( y \) tales que \( \frac{\partial f}{\partial x}(x, y)=0 \) y \( \frac{\partial f}{\partial y}(x, y)=0 \) a. \( f(x, y)=x^{2}+4 x y+y^{2}
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• f(x)=36-x^(2) Find all the real zeros
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• Subtract. Simplify the result if possible. (5x^(2)+7x)/(x-1)-(x+11)/(x-1)
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• Solve the equation. If necessary, rou 4^(x+8)=3^(x)
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  Part III: Solve the following 3. Compute \( \frac{d}{d x}\left(\int_{\cos x}^{2} e^{-t^{2}} d t\right) \cdot[3 \) pts \( ] \)
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  Para cada función hallar los valores de \( x \) y los de \( y \) tales que \( \frac{\partial f}{\partial x}(x, y)=0 \) y \( \frac{\partial f}{\partial y}(x, y)=0 \) a. \( f(x, y)=x^{2}+4 x y+y^{2}-4
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  Verify the identity. (Simplify your answers completely.) \[ \begin{array}{l} \frac{5 \tan x+6 \tan y}{1-\tan x \tan y}=\frac{6 \cot x+5 \cot y}{\cot x \cot y-1} \\ \frac{5 \tan x+6 \tan y}{1-\tan x \t
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  Question 5 1 pts Solve using Laplace Transforms \[ \begin{array}{l} y^{\prime \prime}+9 y=2 \sin (2 t), y(0)=0, y^{\prime}(0)=-1 \\ y=\frac{2}{3} \sin 2 t-\frac{3}{5} \sin 3 t \\ y=\frac{2}{5} \sin 2
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  Question 6 \( 0.5 \mathrm{pts} \) Find \( Y(s) \) for the initial value problem \[ y^{\prime \prime}+6 y=4 t^{2}-3, y(0)=0, y^{\prime}(0)=-7 \] \( \frac{-7 s^{3}-3 s^{2}-8}{s^{3}\left(s^{2}+6\right)}
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  (1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-11 y^{\prime \prime}+18 y^{\prime}=32 e^{x} \] \[ \begin{array}{l} y(0)=11, \quad y^{\prime}(0)=20, \quad y^{\prime \prim
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  Find \( a .\left(\frac{\partial w}{\partial x}\right)_{y} \) and \( b .\left(\frac{\partial w}{\partial z}\right)_{y} \) at the point \( (x, y, z)=(2 \pi,-2,-\pi) \) if \( w=x^{2}+y^{2}+z^{2} \) and \
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  6. Considere la función \( W=f(x, y) \), donde \( x=u-v, \quad y=v-u \). Verificar que \( \frac{\partial W}{\partial u}+\frac{\partial W}{\partial v}=0 \).
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  \( \begin{aligned} f(x, y)=y \cos (x y), \quad(0,1), \quad \theta=\frac{\pi}{3} \\ D_{\mathbf{u}} f(0,1)=-\frac{11}{5} x\end{aligned} \)
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  Differentiate \( y=x^{3} \sin x \tan x \). Answer: \( y^{\prime}=3 x^{2}(\sin (x) \tan (x))+(\cos (x) \tan (x))+6 x(\sin (x) \cos (x)) \)
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• 4. Solve the following differential equations: (a) xy′ + y = −xy2 (b) y′ + 2/x (*y = y3 /x2
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