Need Help?

  • Notes
  • Comments & Questions

Q1:

Given: $$f(x, y)=-y i+x j$$

Req: Graphing?

Sol: $$x, y \rightarrow R^{2} $$

$$\begin{array}{l}{(x, y)} \\ {(1,0)} \\ {(-1,0)} \\ {(2, 2)} \\ {(3,0)} \\ {(0,3)} \end{array} | \begin{array} {l}{f(x, y)} \\ {\langle 0,1\rangle} \\ {\langle0,-1\rangle} \\ {\langle -2 ,2\rangle} \\ {\langle 0, 3 \rangle} \\ {\langle -3 , 0 \rangle} \end{array} $$

Q2:

Given: $$f(x, y)=y \sin (x y)$$

Req: $$\nabla f$$

Sol: $$\nabla f=\left\langle f_{x}, f_{y}\right\rangle$$

(1) $$f_{x}=y^{2} \cos (x y)$$

(2) $$f_ y=\sin (x y)+x y \cos (x y)$$

(3) $$\nabla f=\left\langle y^{2} \cos (x y), \sin (xy)+x y \cos (x y)\right\rangle$$

No comments yet

Join the conversation

Join Notatee Today!