Question

AP Calculus: Slope Fields/ Separate Variables
Find the equation of the curve, given the derivative and the indicated point on the curve.
dy/dx=1/(x+2)

Answer 1

point on graph is (0,1)

Answer 2

@SithsAndGiggles

Answer 3

Can you find the general antiderivative of 1/(x+2)?

Answer 4

u mean integral?

Answer 5

@tkhunny

Answer 6

You can call it "Steve" if you want. That's what you need to solve it.

What do you get?

Answer 7

soo far this is what I got \[\int\limits_{}^{} dy = \int\limits_{}^{} \frac{ 1 }{ x+2 } dx\]
\[y=\ln \left| x+2 \right| + C\]

Answer 8

@tkhunny

Answer 9

Perfect. Why didn't you do that in the first place? Maybe you did and you just weren't sharing.

Okay, now substitute the known initial values and solve for "C".

x = 0
y = 1

Answer 10

how do i get rid of ln though

Answer 11

Why do you want to do that? Are you a logarithmist? Just solve it with whatever it is.

Answer 12

ok so i got \[1=\ln \left| 2 \right| + C\]

Answer 13

2 > 0

Simplify and solve for C. You'll be done.

Answer 14

2>0? I still dont get it how do i get C by itself?

Answer 15

wouldn't i times ln by e to cancel out "ln"? @tkhunny

Answer 16

or put in a \[ \pm\]

Answer 17

That makes absolutely no sense at all. It seems as though you are throwing dice to try to solve this.

1) Never use "times" like that again. It's multiplication. Multiply things.
2) Just solve for C. Why are you resisting?

1 = ln(2) + C

C = 1 - ln(2)

Why isn't that done? Is there a federal mandate to banish all logarithms?

Answer 18

ok ty :)

Answer 19

@tkhunny can you help me with another one?

Answer 20

Only if you post it and promise to quit hating on logarithms. ;-)