Question

1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and...

1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and S(x, y, z) = (2y − z, x − z, y + 3x). Use matrices to find the composition S ◦ T.

2. Find an equation of the tangent plane to the graph of x 2 − y 2 − 3z 2 = 5 at (6, 2, 3).

3. Find the critical points of f(x, y) = (x 2 + y 2 )e −y .

4. Find the length of the parabola y = x 2 between the origin and the point (1, 1).

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