Advanced Math Archive: Questions from July 13, 2022
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solve the exact differential equation (tan y-2)dx+(xsec^2(y+1/y)dy=0 , y(0)=1
5. \( (\tan y-2) d x+\left(x \sec ^{2} y+\frac{1}{y}\right) d y=0, \quad \) y \( (0)=1 \)1 answer -
1 \[ y^{\prime \prime \prime}-4 y^{\prime \prime}+y^{\prime}+6 y=8 \cos x+18 x+3, y(0)=-\frac{6}{5}, y^{\prime}(0)=-11, y^{\prime \prime}(0)=\frac{11}{5} \] \( y^{\prime \prime \prime}+2 y^{\prime \p1 answer -
solve y''-y=0, y(0)=1, y'(1)=0
15) Solve \( y^{\prime \prime}-y=0, \quad y(0)=1, \quad y^{\prime}(1)=0 \)3 answers -
Solve y^(4)+y=0. Hint: m^4+1=(m^2+1)^2-2m^2
17) Solve \( y^{(4)}+y=0 \). Hint: \( m^{4}+1=\left(m^{2}+1\right)^{2}-2 m^{2} \)1 answer -
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35
35. Maximize \( P=20 x+30 y \) subject to \[ \begin{array}{rr} 0.6 x+1.2 y \leq & 960 \\ 0.03 x+0.04 y \leq & 36 \\ 0.3 x+0.2 y \leq & 270 \\ x, y \geq & 0 \end{array} \]1 answer -
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2. Given \( f(x, y)=e^{2 x^{2}+3 y^{2}} \), find and simplify \( f_{x x}(x, y), f_{y y}(x, y), f_{x y}(x, y) \), and \( f_{y x}(x, y) \).1 answer -
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Pleas step-by-step neatly
Determine how the following lines interact. a. \( (x, y, z)=(-2,1,3)+t(1,-1,5) ;(x, y, z)=(-3,0,2)+s(-1,2,-3) \) b. \( (x, y, z)=(1,2,0)+t(1,1,-1) ;(x, y, z)=(3,4,-1)+s(2,2,-2) \) C. \( x=2+t, y=-1+23 answers -
3 answers
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Calculate the local maximum and minimum values, and point or points chairs of the function. Please include all step
5. Calcule los valores máximo y mínimo locales, y punto o puntos sillas de la función. \[ f(x, y)=x^{3}-6 x y+8 y^{3} \]1 answer -
Compute the directional derivative of the function at the given point in the direction of the vector v. All steps Please!!!!!
4. Calcule la derivada direccional de la función en el punto dado en la dirección del vector \( v \). \[ g(r, s)=\tan ^{-1}(r s), \quad(1,2), \quad \mathbf{v}=5 \mathbf{i}+10 \mathbf{j} \]1 answer -
(1 point) Let \( f(x, y)=6 x^{4} y^{3} \). Then \[ \begin{aligned} f_{x}(x, y) &=\\ f_{x}(-2, y) &=\\ f_{x}(x, 4) &=\\ f_{x}(-2,4) &=\\ f_{y}(x, y) &=\\ f_{y}(-2, y) &=\\ f_{y}(x, 4) &=\\ f_{y}(-2,4)1 answer -
(1 point) Let \( f(x, y, z)=\frac{x^{2}-3 y^{2}}{y^{2}+3 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]1 answer -
3. Use the chain rule to find the indicated partial derivatives. Please allsteps!!!!
Use la regla de la cadena para calcular las derivadas parciales que se indican. \[ \begin{array}{l} T=\frac{v}{2 u+v}, \quad u=p q \sqrt{r}, \quad v=p \sqrt{q} r \\ \frac{\partial T}{\partial p}, \fra1 answer -
20. Let \( f(x)=x-5 \) and \( g(x)=(x-1)^{2} \). Evaluate for each composite function. a) \( y=f(g(3)) \) b) \( y=g(f(3)) \) c) \( y=g(g(3)) \) d) \( y=f(f(3)) \) e) \( y=f^{-1}(g(3)) \)1 answer -
Sección \( 8.1 \) Longitud de arco 1. Define longitud de arco. ¿Cómo se calcula? 2. Encuentra la longitud del segmento de recta desde el punto \( A=(0,1) \) hasta el punto \( B=(5,13) \). Graficar.0 answers -
Consider the following functions on \( \mathbf{R}^{2} \) : (i) \( f_{1}(x, y)=x \), (ii) \( f_{2}(x, y)=-x \) (iii) \( f_{3}(x, y)=y \), (iv) \( f_{4}(x, y)=-y \) (v) \( f_{5}(x, y)=x+y \) (vi) \( f_{1 answer -
Consider the following functions on \( \mathbf{R}^{2} \) : (i) \( f_{1}(x, y)=x \), (ii) \( f_{2}(x, y)=-x \) (iii) \( f_{3}(x, y)=y \), (iv) \( f_{4}(x, y)=-y \) (v) \( f_{5}(x, y)=x+y \) (vi) \( f_{1 answer -
Consider the following functions on \( \mathbf{R}^{2} \) : (i) \( f_{1}(x, y)=x \), (ii) \( f_{2}(x, y)=-x \) (iii) \( f_{3}(x, y)=y \), (iv) \( f_{4}(x, y)=-y \) (v) \( f_{5}(x, y)=x+y \) (vi) \( f_{1 answer