Quiz 4 Prep

Question 1

tell me abt functions of 2 variables.

Answer 1

Ex. f(x,y) = x^2 + y ^2
f(1,3) = 1^2 + 3 ^2 = 10
Plug in a point in R^2 and you get a number

Question 2

tell me abt funciton of 3 variables

Answer 2

Ex. f(x,y,z) = e^xy + z
f(-1,-2,5) = e^(-1)(-2) + 5
Plug in a point in R^3 and you get a number

Question 3

difference b/w domains in multi variable function and Calc A functions.

Answer 3

Multi varaible functions have bigger domains. Calc A it’s x-axis, Multi variable functions are the xy-plane

Question 4

graphs vs levels sets

Answer 4

graphs: include domain and range of functions
Level sets: have subsets of the domain only. Every function has infinitely many level sets.

Question 5

general formulat for tangent plane

Answer 5

z = f_x(a,b)*(x-a) + f_y(a,b) * (y-b) + c. c = f(a,b)

Question 6

what does this represent: z = x^2 + y^2

Answer 6

elliptical paraboliod.

Question 7

what does this represent: z=x^2 - y^2

Answer 7

hyperbolic paraboloid

Question 8

what does this represent: ax^2 + by^2 + cz^2 = 1. Notice same signs!

Answer 8

ellipsoid. it looks like a football

Question 9

what does this represent: -ax^2 + by^2 + cz^2 = 1. Notice the different signs.

Answer 9

One sheeted hyperboloid. It’s like a cube but with dents in all sides.

Question 10

what does the variable alone represent?

Answer 10

where the function faces. For example if its a paraboliod and the function = x, it opens on the x axis. Traditionally they face or open toward the z axis so just make a visual in your head.

Question 11

what does this represent: -ax^2 - by^2 + cz^2 = 1. Notice the different signs.

Answer 11

two sheeted paraboloid. it looks like two plates far from each other.

Question 12

what does a level set look like algebraically?

Answer 12

f(x,y) = c. C is a constant/integer. you plug in points into the function