1. Find the gradient vector field of the function $f$ ; sketch the vector field (at points $(0, 0), (\pm 1, 0), (0, \pm 1)$ , $(\pm 1, 1)$ , and $(\pm 1, - 1))$ for (i) and (ii): (i) $f (x, y) = - x^{2} + y^{2}$ (ii) $f (x, y) = ln (x^{2} + y^{2})$ (iii) $f (x, y, z) = x^{2} + 2 y^{2} + 3 z^{2}$ (iv) $f (x, y, z) = tan (2 x - 3 y + 4 z)$

Question

1. Find the gradient vector field of the function

f

; sketch the vector field (at points

(0, 0), (\pm 1, 0), (0, \pm 1)

,

(\pm 1, 1)

, and

(\pm 1, - 1))

for (i) and (ii): (i)

f (x, y) = - x^{2} + y^{2}

(ii)

f (x, y) = ln (x^{2} + y^{2})

(iii)

f (x, y, z) = x^{2} + 2 y^{2} + 3 z^{2}

(iv)

f (x, y, z) = tan (2 x - 3 y + 4 z)

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(Solved): 1. Find the gradient vector field of the function f; sketch the vector field (at points (0,0),(1, ...