Other Math Archive: Questions from October 06, 2022
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2 answers
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Solve the differential equation dx + ex dy = 0 using separable equations
Resuelva la ecuación diferencial \( d x+e^{3 x} d y=0 \) utilizando ecuaciones separables2 answers -
Determine if -2x2y+y2= 1 is an implicit solution of 2xydx=(x²-y)dy = 0
Determine si \( -2 x^{2} y+y^{2}=1 \) es una solución implícita de \( 2 x y d x=\left(x^{2}-y\right) d y=0 \)2 answers -
Given that \( \left|\begin{array}{lll}a & b & c \\ d & e & f \\ g & h & i\end{array}\right|=1 \), find \( \left|\begin{array}{ccc}a & b & c \\ 3 d & 3 e & 3 f \\ g+4 a & h+4 b & i+4 c\end{array}\right2 answers -
9. Find out \( \mathrm{df}(\mathrm{x}, \mathrm{y}, \mathrm{z}) \) if \( \mathrm{f}(\mathrm{x}, \mathrm{y}, \mathrm{z})=\frac{x y^{3}}{z}-3 x y^{2} z^{4}+\log _{3}(7 x+y)+5 z-1 \) 10. Find out \( \math2 answers -
6. Demuestre que la serie \[ \sum_{n=1}^{\infty} \frac{x}{n\left(1+n x^{2}\right)} \] converge uniformemente en \( \mathbf{R} \). 7. (a) Demuestre que la serie \[ \sum_{n=0}^{\infty} 2^{n} \operatorna2 answers