In section 1.3 we saw that the autonomous differential equation m dv dt = mg − kv, where k is a positive constant and g is the acceleration due to gravity, is a model for the velocity v of a body of mass m that is falling under the influence of gravity. because the term −kv represents air resistance, the velocity of a body falling from a great height does not increase without bound as time t increases. use a phase portrait of the differential equation to find the limiting, or terminal, velocity of the body. lim v(t -> infinity)=

Step-by-step explanation:

Firstly its necessary to put the autonomous DE in its normal form to get

To get the critical point we solve

g -

The critical point is 

and

from the phase portrait we observe that the critical point

v =  is stable

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!