Calculus Archive: Questions from August 17, 2022
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\( f(x, y)=\left\{\begin{array}{ll}\frac{6 x^{3}+x^{4}-y^{3}}{3 x^{2}+y^{2}} & \text { if }(x, y) \neq(0,0) \\ 0 & \text { if }(x, y)=(0,0)\end{array}\right. \)1 answer -
Given \( f(x, y)=6 x^{4}+5 x^{2} y^{6}-6 y^{3} \) \( f_{x}(x, y)=\mid \) \( f_{y}(x, y)= \) \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \)1 answer -
I. Determine la longitud del arco en el intervalo dado a) \( r(t)=i+t^{2} j+t^{3} k ;[0,2] \) b) \( r(t)=\langle 4 t,-\cos t, \operatorname{sen} t\rangle ;\left[0, \frac{3 \pi}{2}\right] \)1 answer -
II. Determine e interprete la curvatura K de la curva en el valor del parĂ¡metro dado a) \( r(t)=t^{2} i+j ; t=2 \) b) \( r(t)=\left\langle 3 t, 2 t^{2}\right\rangle \) en el punto \( (-3,2) \) c) \(1 answer -
1 answer
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3 answers
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Given \( f(x, y)=-6 x^{3}+x^{2} y^{6}+6 y^{4} \), fi \[ \begin{array}{l} f_{x}(x, y)=-18 x^{2}+2 x y^{6} \\ f_{y}(x, y)=6 x^{2} y^{5}+24 y^{3} \end{array} \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]1 answer -
3 answers