Melody

OR maybe this was the question

$$f(x)=3x+\frac{3}{x}=\frac{3x^2+3}{x}\\\\
f(x+h)=3(x+h)+\frac{3}{x+h}\\\\
f(x+h)-f(x)=3x+3h+\frac{3}{x+h}-3x-\frac{3}{x}\\\\
f(x+h)-f(x)=3h+\frac{3}{x+h}-\frac{3}{x}\\\\
f(x+h)-f(x)=\frac{3h(x+h)x+3x-3(x+h)}{x(x+h)}\\\\
f(x+h)-f(x)=\frac{3h(x+h)x-3h}{x(x+h)}\\\\
\left[f(x+h)-f(x)\right]\div h=\frac{3(x+h)x-3}{x(x+h)}\\\\$$

Now taking it the extra logical step

$$\left[f(x+h)-f(x)\right]\div h=\frac{3(x+h)x-3}{x(x+h)}\\\\$$

limit as h tends to 0 =   $$\frac{3x^2-3}{x^2}$$

Now, if I didn't make any mistakes this is the derivative of the original equation. And it is!   

NOW can someone tell me how to write limit as h tends to 0 in latex please?

I am just learning from Alan's post - Thank you Alan. 

$$arg(z+2)=\frac{\pi}{6}\\\\
arg(x+iy+2)=\frac{\pi}{6}\\\\
arg((x+2)+iy)=\frac{\pi}{6}\\\\
tan\left(\frac{\pi}{6}\right)=\frac{y}{x+2}\\\\
\frac{1}{\sqrt3}=\frac{y}{x+2}\\\\
y=\frac{x+2}{\sqrt3}\\\\$$

See the diagram at this address - I haven't work out how to insert pictures yet.

http://gyazo.com/7bb85148a5e4c5c1cb6bddbfc206bbea

Thanks for 'having a go' unknown - I like to see that.  

But, the second answer is correct.

arc cos is the same as inverse cos

$$acos\theta=cos^{-1}\theta$$

You have to look for a number that goes inot the top and into the bottom without any remainders.

Then you divide the top and bottom by that number.  

Hi bioschip,

I am glad that 'you do so good in math today' 

Yes, yes, thanks Rom, I could see that it would work! 

What is a taquito?  

I think that Bob dropped everything and sea gulls and bower birds stole all the golf b***s.

You know different species of Bower Birds collect different coloured objects. In Australia we have a Great Bower Bird and the male likes to collect white objects.  His bower is heavily decorated - he especially likes bleached bones.  I am sure he'd like to add a golf ball or 2 as well.  

Technically speaking 21! means 1x2x3x4x5x6x7......x21

so the answer is 4/21

I know that is what you meant.

Thanks for answering - why don't you join up so that you can get proper recognition. 

Thanks Kitty