Other Math Archive: Questions from March 11, 2023
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2 answers
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The differential equation \( y^{\prime}=\sqrt{2 x-y+1}+2 \) has the solution \( y=\frac{2(2 x-y+1)^{\frac{3}{2}}}{3}-x+c \) a. b. \( 2 x-y+1=\left(\frac{c-x}{2}\right)^{2} \) c. \( y=\left(\frac{c-x}{2 answers -
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4 answers
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Suppose \( f(x, y)=\left(x^{2}+y^{2}\right)^{\frac{1}{3}} \). Show \[ f_{x}(x, y)=\left\{\begin{array}{l} \frac{4 x}{3\left(x^{2}+y^{2}\right)^{\frac{1}{3}}},(x, y) \neq(0,0) \\ 0,(x, y)=(0,0) \end{ar2 answers -
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2 answers
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Question-2: For \( x \varepsilon R^{l} \) and \( y \varepsilon R^{l} \), define \[ \begin{array}{l} d_{1}(x, y)=(x-y)^{2} \\ d_{2}(x, y)=\sqrt{x-y} \\ d_{3}(x, y)=\left|x^{2}-y^{2}\right| \\ d_{4}(x,2 answers -
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