Quiz 3 Prep

Question 1

generally, what does a paraboliod equation look like w/o getting into symbols?

Answer 1

Started with x, y and z. Two of them are squared, then usually solve for the one that isn’t squared.

Question 2

Difference b/w eliptical paraboliod vs hyperbolic paraboliod algebarically

Answer 2

x,y or z = ± A(x,y,z)^2 ± B(x,y,z)^2

Same signs elipicaly paraboliod
Different signs hyperbolic paraboliod

Question 3

What if the whole paraboliod equation is squared?

Answer 3

Get RHS equal to a pos constant. ±Ax^2 ±By^2 ±Cz^2 = d. If all the signs are positive eplisiod and if all are negative, function doesnt exist

Question 4

how to do we take the limit of a vector function?

Answer 4

Take limit of each function

lim r(t)<f(t),g(t),h(t)> = lim< lim f(t),lim g(t),lim h(t)>

Question 5

definition of derivative for vector function

Answer 5

r’(t) = r(t+h) - r(h) / h

lim_(h -> 0)

Question 6

what’s a cute fact abt r’(t)?

Answer 6

if r(t)=<f(t), g(t), h(t)> then r’(t) = <f’(t), g’(t), h’(t)>