Advanced Math Archive: Questions from April 03, 2023
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Partial derivative. Compute \( f_{x y x z y} \) for \[ f(x, y, z)=y \sin (x z) \sin (x+z)+\left(x+z^{2}\right) \tan y+x \tan \left(\frac{z+z^{-1}}{y-y^{-1}}\right) \]2 answers -
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differential equations ch 4 please solve all !
Q3 \( \quad y^{(5)}-y^{(3)}=e^{x}+2 x^{2}-5 \) Q4 \( \quad y^{\prime \prime}+4 y=3 x \cos (2 x) \) Q5 \( y^{(3)}-y^{\prime \prime}-12 y^{\prime}=x-2 x \cdot e^{-3 x} \) Q6. \( \quad y^{\prime \prime}-2 answers -
EVALUATE ( GAMMA )
(g) \( \int_{0}^{\infty} e^{-h^{2} x^{2}} d x \) (h) \( \int_{0}^{\infty} e^{-y^{\left(\frac{1}{m}\right)}} d y \) (i) \( \int_{0}^{1}\left\{\ln \left(\frac{1}{t}\right)\right\}^{-\frac{1}{2}} d t \)2 answers -
1. Given the set, what is the subset of the rational numbers within this set: 8. For all real numbers a and b, by definition of subtraction the following statement is true or false: 9. Resolve.
1. Dado el conjunto \( \left\{-4,0, \frac{1}{\sqrt{16}}, 0.56, \sqrt{3}, \emptyset, \pi,-2,-\frac{1}{2}, 15\right\} \) es subconjunto de los números racionales dentro de este conjunto es: a. \( \math2 answers -
12. Determine if -3 is a solution of the equation 2x-5=-11. 15. Resolve.
12. Determine si -3 es solución de la ecuación \( 2 x-5=-11 \). a. \( x=-2 \) b. -3 no es solución de la ecuación. c. -3 es solución de la ecuación. d. \( -11=11 \). e. La ecuación es equivalen2 answers -
For all real numbers a and b, by definition of subtraction the following statement is true or false:
8. Para todos los números reales a \( \mathrm{y} \) b, por definición de sustracción es \( (\mathrm{C}) \) cierto \[ \mathbf{a}-\mathbf{b}=\mathbf{a}+(-\mathbf{b}) \] a. Cicrto b. Falso2 answers -
6. Define \[ T\left(x^{*}, y^{*}\right)=\left(\frac{x^{*}-y^{*}}{\sqrt{2}}, \frac{x^{*}+y^{*}}{\sqrt{2}}\right) . \] Show that \( T \) rotates the unit square, \( D^{*}=[0,1] \times[0,1] \).2 answers -
10. \( y^{\prime \prime}+y^{\prime}+\frac{5}{4} y=g(t) ; \quad y(0)=0, \quad y^{\prime}(0)=0 ; \quad g(t)=\left\{\begin{array}{ll}\sin t, & 0 \leq t2 answers -
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Muestre que si m 4 + 4 n es primo, entonces m es impar y n es par (excepto en el caso de m = n = 1 )0 answers
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