Advanced Math Archive: Questions from August 26, 2022
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1 answer
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\( \frac{2 \sec ^{2} x-2 \tan ^{2} x}{\csc x}=\sin 2 x \sec x \) \[ \frac{1-2 \sin ^{2} x}{\sin x+\cos x}+2 \sin \frac{x}{2} \cos \frac{x}{2}=\cos x \]0 answers -
c) If \( u=\sin ^{-1}\left(\frac{x}{y}\right) \), find the value of \( x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y} \). [8]1 answer -
suelva \( 2 x^{2} y d x=\left(3 x^{3}+y^{3}\right) d y \) \[ y^{9}=c\left(x^{3}+y^{3}\right)^{2} \] \[ \frac{c}{y^{9}}=\left(x^{3}+y^{3}\right)^{2} \] \[ \frac{2}{3} \ln \left(x^{3}+y^{3}\right)^{2}=c1 answer -
The solution to \( x y^{\prime}+2 y=e^{3 x} \) is Select one: a. \( y=\left(x e^{3 x}-1 / 3 e^{3 x}+3 C\right) / 3 x^{2} \) b. \( y=x e^{3 x}-3 e^{3 x}+C \) c. \( y=e^{3 x}-\left(e^{3 x} / x\right)+(c1 answer -
Find the tangent plane of the following surfaces with the point given.
- Encuentra la ecuación del plano tangente de las siguientes superficies en el punto dado: - \( z=2 x^{2}+y^{2}-5 y,(1,2,-4) \) - \( z=e^{x-y},(2,2,1) \) - \( z=x \sin (x+y),(-1,1,0) \)1 answer -
1. Obtain the binomial form to the following equation: 2. Prove that if p(x) = a0+a1x+· · ·+anxn is a polynomial with coefficients (that is, ai ∈ R, ∀i) and z0 is a root of p, so z0 is also a r
E.7 Obtener en forma binomial todas las soluciones de las siguientes ecuacio- \[ z^{4}=2, \quad z^{3}=\frac{1}{8} i, \quad z^{6}=-1 \] E.24 Probar que si \( p(x)=a_{0}+a_{1} x+\cdots+a_{n} x^{n} \) e1 answer -
\( \frac{d^{2} y 2}{d t^{2}}=-k_{1} y_{2}-b_{2}\left(\frac{d y_{2}}{d t}-\frac{d y_{2}}{d t}\right) \times 2 y \) \[ m_{2} \frac{d^{2} y 2}{d t^{2}}=-k 2 y^{2}-b_{2} \frac{d y_{2}}{d t^{2}}-\frac{d y}0 answers