Calculus Archive: Questions from January 17, 2023
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Let \( w=g(x, y, z) \) be the set of all ordered pairs \( (P, w) \) such that \[ w=g(x, y, z)=\sqrt{4-x^{2}-y^{2}-z^{2}} \] Find 10. \( g\left(\frac{1}{2} x, \frac{1}{2} y, \frac{1}{2} z\right) \) A.2 answers -
If \( \sin x=-\frac{1}{7} \) and \( \tan y=\frac{2}{5} \) where \( x \) and \( y \) are in the interval \( [\pi / 2,3 \pi / 2] \), What are the exact values of the following trigonometric ratios? (Mat2 answers -
60. Find the values of \( \lambda \) for which \( y=e^{\lambda x} \) satisfies the equation \( y+y^{\prime}=y^{\prime \prime} \).2 answers -
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Ejemplo 3: Halle el volumen de la región solida limitada por \( z=f(x, y)=e^{-x^{2}} \) y los planos, \( z=0, y=0, x=1 \) y \( y=x \) Grafica delsólido Proyeccion en el plano \( x y \)2 answers -
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2. Calcule los siguientes límites: \( \lim _{(x, y) \rightarrow(0,0)}(x+y) \sqrt{x^{2}+y^{2}} \operatorname{sen}\left(\frac{1}{\sqrt{x^{2}+y^{2}}}\right) \)2 answers -
2. Calculate \( y^{\prime} \). (a) \( y=\left(x+\frac{1}{x}\right)^{5} \) (b) \( G(x)=\frac{x^{2}}{1+e^{x}} \)2 answers -
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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 -
Ficoja lo contentacibh rorrecta, Thene 3 intentios psra trabajaris, se conwiderara la de mabror puntuacion para promedio de ia clase. \( [-/ 2 \) Points] LARCALC11 \( 4.1 .042 \) Find the particutar s2 answers -
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Find the first partial derivatives of the function. \[ f(x, y)=x-5 x^{3} y^{6} \] As a list: \[ f x(x, y), f y(x, y)= \] i. \( x-16 x^{3} y^{2},-8 x^{4} y \) ii. \( y-15 x^{3} y^{2},-18 x^{4} y \) iii2 answers -
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