Problem 1
Let a level curve of \(z=f(x, y)\) be described by \(x=g(t)\), \(y=h(t) .\) Explain why \(\frac{d z}{d t}=0\)
Problem 1
What is the difference between a constant and a coefficient?
Problem 1
Describe in your own words the difference between boundary and interior points of a set.
Problem 1
T/F: If \(f(x, y)\) is differentiable on \(S\), the \(f\) is continuous on \(S\).
Problem 1
What is the difference between a directional derivative and a partial derivative?
Problem 2
Use your own words to describe (informally) what \(\lim _{(x, y) \rightarrow(1,2)} f(x, y)=17\) means.
Problem 2
T/F: A point \(P\) is a critical point of \(f\) if \(f_{x}\) and \(f_{y}\) are both 0 at \(P\).
Problem 2
Explain how the vector \(\vec{v}=\langle 0.6,0.8,-2\rangle\) can be thought of as having a "slope" of -2 .
Problem 2
The graph of a function of two variables is a __________.
Problem 3
Give an example of a closed, bounded set.
