1.Indicate True or False:
(a) In three-dimensional space, if two lines L1 and L2 do not intersect, then there cannot be a

a plane containing both L1 and L2.

(b) For vectors a and b, we always have a × projab = 0.

(c) The curve given by r = costi + sintj + (1 + t2)k never intersects the xy-plane.

(d) If r1 and r2 are smooth parametrizations of the same curve C, then the curvature κ at a point P on C is the same whether it is computed using r1 or r2.

(e) The graph of f(x, y) = x2 + y2 is a hemisphere.

(f) Every continuous function f(x, y) on domain D = {(x, y) | 0 < x < 1, 0 < y < 1}

attains an absolute maximum on D.

(g) To switch the order of integration for a continuous function f(x, y), we use

1x 1y
∫ ∫ f(x,y)dydx = ∫ ∫ f(x,y)dxdy

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(h) To evaulate the integral by changing from rectangular to cylindrical coordinates for a continuous functions f(x, y, z), we use

2 √4−x2 xy

f(x,y,z)dzdydx = ∫

2π 2 ∫

∫

r2 cosθsinθ

∫ ∫ 2 ∫ −2 −√4−x 0

f(rcosθ,rsinθ,z)r dzdrdθ

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