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Math 251 Calculus III Quiz

Books, notes, and calculators are not allowed . Show all your work. Good Luck!

1. (4 pts) Given , where x = sin(st) and

[ Do not simplify ]

2. (4 pts) Given f (x, y) = ln (x + 2y),

Find the directional derivative Duf at the point (1, 1) in the direction .

3. (7 pts) Given

(a). Find the linearization L (x, y) at the point (4, 0).

(b)Use the linearization L (x, y) from part (a) to approximate the value of f(4.3,-0.2).

[ Simplify as much as possible ( converting decimals to fractions at some point will help).
Remember one of the reasons for using linearizations is to have a decent way to approximate values without a calculator .]

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