Advanced Math Archive: Questions from December 29, 2022
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only 24 plz
24. \( y=\sin x, y=\cos x, 0 \leqslant x \leqslant \pi / 4 ; \quad \) about \( y=-1 \) 25. \( y=x^{3}, y=0, x=1 ; \quad \) about \( x=2 \) 26. \( x y=1, y=0, x=1, x=2 ; \) about \( x=-1 \)2 answers -
4) (20 pts) Solve \[ \frac{d^{2} y}{d y^{2}}+\lambda y=0, \quad y(0)=y(2 \pi), \quad y^{\prime}(0)=y^{\prime}(2 \pi) \]0 answers -
4. Consider the function \( f(x, y) \) defined by \[ f(x, y)=\left\{\begin{array}{cc} \frac{x y\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}} & \text { if }(x, y) \neq(0,0) \\ 0 & \text { if }(x, y)=(0,0) \en2 answers -
2 answers
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1. Find the equation of the tangent plane to the surface \[ z=f(x, y) \quad \text { at } \quad\left(x_{0}, y_{0}, z_{0}\right)=\left(x_{0}, y_{0}, f\left(x_{0}, y_{0}\right)\right) . \] (a) \( f(x, y)0 answers -
explain it in a clear form.
1. Find the equation of the tangent plane to the surface \[ z=f(x, y) \quad \text { at } \quad\left(x_{0}, y_{0}, z_{0}\right)=\left(x_{0}, y_{0}, f\left(x_{0}, y_{0}\right)\right) . \] (a) \( f(x, y)2 answers