Q8·Section II (Mathematics)·8 of 145The Jacobian of fff at the originf:R2→R3f:\mathbb{R}^2\to\mathbb{R}^3f:R2→R3 is defined as f(u,v)=(u2−5v,ve2u,2u−log(1+v2))f(u,v)=\bigl(u^2-5v, ve^{2u}, 2u-\log(1+v^2)\bigr)f(u,v)=(u2−5v,ve2u,2u−log(1+v2)). Then Df(0,0)=Df(0,0)=Df(0,0)= OptionsA(012−510)\left(\begin{smallmatrix}0&1&2\\-5&1&0\end{smallmatrix}\right)(0−51120)B(−5−51120)\left(\begin{smallmatrix}-5&-5\\1&1\\2&0\end{smallmatrix}\right)(−512−510)C(0−50120)\left(\begin{smallmatrix}0&-5\\0&1\\2&0\end{smallmatrix}\right)(002−510)D(01−5110)\left(\begin{smallmatrix}0&1&-5\\1&1&0\end{smallmatrix}\right)(0111−50)Pick an option to check your answer.Show answerShow solution Report a problem with this question← Q7All questionsQ9 →Keyboard: A–D answer · S solution · ←/→ previous/next