# Raptors Quiz

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Math 241 Fall 2011

Quiz 2

Name:

READ: (Inspired by http://www.xkcd.com/135) You are stranded hanging from a tree in the

jungle on the side of a steep hill given by the equation g(x, y, z) = x + y - z = 0. Your location

is 18 feet above the origin (i.e. at the point (0, 0, 18)).

Unfortunately this jungle you are in is infested with savage velociraptors who know how to use

Lagrange multipliers when necessary. Show your work and circle your answers. Justify your

answers whenever possible. No calculators. Remember, raptors do not know fear.

1. (1 point) Give the formula for the distance squared d2 = f(x, y, z) between a raptor located

at point (x, y, z) and your position (0, 0, 18).

2. (1 point) Compute f and g ( denotes the gradient).

3. (3 points) Use Lagrange multipliers to find the point on the plane which is closest to you.

4. (0 points) (For fun.) What is the distance between you and this closest point? If raptors

can jump 12 feet into the air, will you be able to live? (You can use the fact that

3 < 2.)

Quiz 2

Name:

READ: (Inspired by http://www.xkcd.com/135) You are stranded hanging from a tree in the

jungle on the side of a steep hill given by the equation g(x, y, z) = x + y - z = 0. Your location

is 18 feet above the origin (i.e. at the point (0, 0, 18)).

Unfortunately this jungle you are in is infested with savage velociraptors who know how to use

Lagrange multipliers when necessary. Show your work and circle your answers. Justify your

answers whenever possible. No calculators. Remember, raptors do not know fear.

1. (1 point) Give the formula for the distance squared d2 = f(x, y, z) between a raptor located

at point (x, y, z) and your position (0, 0, 18).

2. (1 point) Compute f and g ( denotes the gradient).

3. (3 points) Use Lagrange multipliers to find the point on the plane which is closest to you.

4. (0 points) (For fun.) What is the distance between you and this closest point? If raptors

can jump 12 feet into the air, will you be able to live? (You can use the fact that

3 < 2.)