Use a computer algebra system to draw a direction field for the differential equation y' = 3y^3 − 12y. Get a printout and sketch on it solutions that satisfy the initial condition y(0) = c for various values of c.

A)For what values of c does the limit L = lim t → [infinity] y(t) exist?

a. c is in [−2, 2]
b. c is in [2, [infinity])
c. c is in [−2, 0]
d. c is in [0, 2]
e. c is in (−[infinity], −2]

B) What are the possible values for this limit L? (Enter your answers as a comma-separated list.) L =

simplest reason is that Infinity is not a number, it is an idea.

So 1∞ is a bit like saying 1beauty or 1tall.

Maybe we could say that 1∞= 0, ... but that is a problem too, because if we divide 1 into infinite pieces and they end up 0 each, what happened to the 1?

In fact 1∞ is known to be undefined.

But We Can Approach It!

So instead of trying to work it out for infinity (because we can't get a sensible answer), let's try larger and larger values of x:

graph 1/x

x 1x

11.00000

20.50000

40.25000

100.10000

1000.01000

1,0000.00100

10,0000.00010

Now we can see that as x gets larger, 1x tends towards 0

We are now faced with an interesting situation:

Step-by-step explanation:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3