Calculus Archive: Questions from January 21, 2023
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Let \( f(x, y)=\frac{x-y}{\sqrt{x+2}-\sqrt{y+2}} \) Find \( \lim _{(x, y) \rightarrow(2,2)} f(x, y) \) (if it exists).2 answers -
4. Show that \( z=\frac{1}{2}\left(e^{y}-e^{-y}\right) \sin x \) satisfies \( \frac{\partial^{2} z}{\partial x^{2}}+\frac{\partial^{2} z}{\partial y^{2}}=0 \).2 answers -
The area of the region enclosed by the figure r = 2sin30 is: a. TT b. π/6 c. π/8 d. 2πt e. π/2
El área de la región encerrada por la figura \( r=2 \sin 3 \theta \) es: \( \pi \) \( \pi / 6 \) \( \pi / 8 \) \( 2 \pi \) \( \pi / 2 \)2 answers -
2 answers
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3. (10 points) Find the general solution of \( \left(\frac{2 x}{y}+y\right)+\left(\frac{x^{2}}{y^{2}}+3 x+\frac{1}{y^{2}}\right) y^{\prime}=0, y>0 \).2 answers -
2 answers
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2 answers
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2 answers