Determine if the expression for r(u, v) with domain d defines a smooth parametrized surface. explain your answer. (your instructors prefer angle bracket notation < > for vectors.) r(u, v) = cos(u), sin(v), 1 , d = {(u, v) | 0 ≤ u ≤ 4π, 0 ≤ v ≤ 4π}

you are playing an adventure game on your computer. you come across a troll who won't let you pass and there is no other way to get to the other side of the river except over the bridge he is guarding.

the troll is a nerd. he takes great delight in watching people struggle with his problems. very few get them. he only gives you one chance and then he changes the puzzle. you have to solve this one.

before you are four blocks. they are numbered 11,6, -7,21.

he tells that the answer he wants is minus and between -1 and - 2. you can use +, -, ×, ÷   ( and ) as many times as you like or no times at all. you don't like the way he's looking at you, but you need to cross the bridge. what do you do?