Melody

Have you tried getting out your protractor and a ruler and drawing them. ?

You will not learn just by being given the answers.

I mucked around with this quite a bit before I came up with a solution.

First I did the division and found   \(f(x)=3(x^2+3)+\frac{3(-3x-5)}{x^2+x-2}\)

If I add    \(-3(x^2+3)\)

then the resulting expression will be  \(  \frac{3(-3x-5)}{x^2+x-2}\)

Now with this latest expression the degree of the numerator is 1 and the degree of the denominator is 2

As x tends to infinity both the numerator and the denominator tend to infinity also but the bottom is approaching infinity at a much faster rate (since the degree is higher.) so the expression will tend to 0 as x tends to infinity.

Hence    one solution is    \(g(x)=-3x^2-9\)

\(\displaystyle \lim_{x\rightarrow\infty}\;f(x)+g(x)=0^-\)

Nice work Gino.

I would have to some work before I found the 1/3 part. 

But the rest all seems reasonable ... I think.

Well then guest, look through the answer carefully and find it!

What you have to do is make a graph of with the number of animals along the bottom and cost up the side.

there will be two straight line graphs. One for each scenario.  There will be a cross over point where they are both the same cost (probably a part of an animal)  But, for any given number of animals, the graph on the top will always be the dearer option. 

Now give it a go.  :)

Please no one answer is full.  

Did you learn anything that time qwerty?

I see you are so grateful when people try to help you that much of the time you cannot even be bothered responding.

Draw it using Desmos

What happened to the question?

I assume it was edited out but there is no edit message ??

I have seen this a bit lately.

Thanks guest,

Yes I know that is what he means but I have to rewrite the question properly before I can think it through.

I just cannot look at those dollar signs and ignore them, I have to physically remove them before I start on the problem.

I'm just not prepared to do that.

If they are too lazy to post their questions the best possible, then I expect they will be far too lazy to learn from any response.

Definitely cannot divide by 0.     LOL

dy/dx for e^x + y = y

Perhaps I do not understand the question. Maybe more than just perhaps  

e^x + y = y

e^x=0

Never happens so you cannot find a tangent.   ???

e^x and also its gradient do approach 0 as x approaches -infinity though. 

Maybe another mathematician should look at this. Maybe my definitions are not quite right.

the question does not make sense to me.