Find the length of the curve

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Reference no: EM131082211

Midterm 1 Review - Math 53, section 213

1. Find the length of the curve given by x = 3t2, y = 2t3, 0 ≤ t ≤ 2.

2. Compute the cross product of (1, 1, -1) and (2, 4, 6). What is the area of the parallelogram spanned by these vectors?

3. Find an equation for the plane passing through (1, 2, -2) that contains the line x = 2t, y = 3 - t, z = 1 + 3t.

4. Evaluate the following limit or show that it does not exist:

lim(x,y)→(0,0)(x3 + y3/x2 + y2).

What about the limit

lim(x,y)→(0,0)(x2 + y2/x2 - y2)?

5. Find all second partial derivatives of f(x, y, z) = xkylzm.

6. Find equations of the tangent plane and the normal line to the surface xy + yz + zx = 3 at the point (1, 1, 1).

7. Find the maximum rate of change of f(x, y) = x2y + √y at the point (2, 1). In which direction does it occur?

8. Find the critical points (local maxima, minima, and saddle points) of the function f(x, y) = x3 - 6xy + 8y3.

Reference no: EM131082211

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