Question

Equilibrium? (Help with concept) Finding eqb visually/graphically , Finding eqb algebraically??

Answer 1

what exactly do you mean by "equilibrium"?

Answer 2

Idk just a concept my professor said to go over and practice graphically algebraically

Answer 3

I'm in Calc I if that helps

Answer 4

LIke I said I'm having my midterm tomorrow so just going over stuff and the list said equilibrium which I do not understand. So the best you can explain will help

Answer 5

i've not really heard this term before in the context of calculus

do you have an example from your lecture notes or textbook?

Answer 6

equilibria?

Answer 7

oh ok I got it, you just need to solve when x_n+1 = x_n

(they can use the variable x, or a, or whatever)

Answer 8

like, for the first example

a_n+1 = sqrt(a)

you just set a = a_n+1 to get

a = sqrt(a)

which is only true for a = 1 or 0

Answer 9

it's just algebra, really

Answer 10

the n+1 disappears?

Answer 11

we substitute a for a_n+1 since a = a_n+1

Answer 12

if it makes it less confusing you can just use a new variable like z or something

a_n+1 = sqrt(a)

becomes

z = sqrt(z) which gives the same result, just make sure to report your answer in terms of a_n or whatever variable is already in the problem

Answer 13

okay so what if numbers were involved?

Answer 14

same concept

Answer 15

?

Answer 16

yeah, you just set a_n+1 and a_n equal and solve, regardless of what else is in the equation

Answer 17

can you just give a quick example with numbers ? :S

Answer 18

Just want to note an example down for reference with actuAl numbers

Answer 19

like, the second example you have has

a_n+1 = 0.33an + 214.5

you just set a_n+1 and an equal to each other to get

a = 0.33a + 214.5 and solve for a

Answer 20

a-214.5=0.33a

Answer 21

I would recommend subtracting 0.33a from both sides and dividing to isolate a

Answer 22

a-0.33a=214.5

Answer 23

good, finish simplifying the left side

Answer 24

6.71E-1a=214.5

a=3.2E2

Answer 25

I would recommend not converting to base 10 notation here

Answer 26

.67 do 214.5/.67=320

Answer 27

like,

a-0.33a

is just 1 - 0.33 which is 0.67a

0.67a = 214.5

a = 214.5/0.67 = 320.149

Answer 28

yes

Answer 29

NOw how about to graphing an equilibria or whatever :S

Answer 30

uh

well since a_n+1 = an you should look for a part of the graph that levels off/flatlines

Answer 31

i think