8. Midterm 1 and Change of Variables

Midterm 1 — Quiz

Test your understanding of midterm 1 with 5 practice questions.

Practice Questions

Question 1

For $f(x,y)=3x^2y-2y^3$, what is $f_x(x,y)$?

Question 2

What is the gradient of $f(x,y)=x^2+y^2$ at $(1,-2)$?

Question 3

What is the equation of the tangent plane to $z=x^2+y^2$ at $(1,2,5)$?

Question 4

What is the directional derivative of $f(x,y)=x+y$ at $(2,3)$ in the direction of $(3,4)$?

Question 5

Evaluate $(x^2-y^2)/(x-y)$ as $(x,y)$ approaches $(1,1)$.