Calculus Archive: Questions from January 04, 2023
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discuss the continuity of the given function
ven function. \[ f(x, y)=\left\{\begin{array}{c} \frac{x^{2}+2 x y^{2}+y^{2}}{x^{2}+y^{2}} \\ 1 \end{array}\right. \]2 answers -
1. Find the general solution of each ofthe following equations. (a) \( y^{\prime \prime}+y^{\prime}+y=x^{2} \). (b) \( y^{\prime \prime}+y=\sin x+e^{-x} \).2 answers -
\( \begin{array}{l}z=f(x, y)=\arctan \left(\frac{x}{y}\right) \\ x=u \cdot \cos v \\ y=u \cdot \sin v\end{array} \Rightarrow \frac{d z}{d u}=? \frac{d z}{d v}=? \)2 answers -
Determinar cuando la serie es absolutamente convergente, condicionalmente convergente o divergente. 1. \( \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{2 n^{2}} \) 2. \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{\s1 answer -
2 answers
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2 answers
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Given \( f(x, y)=-5 x^{5}+4 x^{2} y^{2}+y^{6} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ \begin{array}{l} f_{x y}(x, y)= \\ f_{y y}(x, y)= \end{array} \] Question Help: \( \squar2 answers -
only #5
4.) \( \int_{4}^{10} 5 d x \quad \mid \frac{1}{4} \) 5.) \( \int_{-4}^{0}\left(\sqrt{16-x^{2}}\right) d x \)2 answers