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\displaystyle \begin{array}{lr} \text{ lim }\\ h \rightarrow 0 \\  \end{array} \frac{3x+h}{x+h}.

That produces

$$\displaystyle \begin{array}{lr} \text{ lim }\\ h \rightarrow 0 \\ \end{array} \frac{3x+h}{x+h}$$

Thanks Bertie,

What is the {lr} for?

I wrote a  post today that mentioned seagulls, just as well it wasn't one of those giving your car grief!

http://web2.0calc.com/questions/this-problem-was-on-my-homework-last-night-and-i-just-don-t-know-how-i-m-supposed-to-solve-it

I've been outside cleaning my car Melody, a seagull had made a mess (and you wouldn't believe the extent of the mess) of the roof and windscreen.

As to LaTex I'm certainly not an expert, I just tend to muddle my way through. Muddling my way through this one, the best I can come up with is

\displaystyle \begin{array}{lr} \text{ lim }\\ h \rightarrow 0 \\  \end{array} \frac{3x+h}{x+h}.

That produces

$$\displaystyle \begin{array}{lr} \text{ lim }\\ h \rightarrow 0 \\ \end{array} \frac{3x+h}{x+h}$$

I've tried to make the h arrow 0 smaller, but without success.

thamk-you for replying

175 is 100% 
18% increase means 118% since the numer is growing. 

175x1.18=206.5

Hey There, 

Not sure if a troll, but here goes.


Substitute the numbers: 4 pairs of shoes at 55$ each, so a shirt has to be 45$ each.  (Shoes are 10$ more expensive then a shirt.) 

4x55+2x45= $310

Good Day.

Hi everyone,

There were lots of great answers today from Gman2598, Alan, CPhill, Bertie, Kitty<3, novice, unknown and a number of anonymous people. Thank you very much.

I think all member questions and most anonymous questions have been answered.  I have checked as many of those answers as possible and given a tick to almost all of them.  I am starting to burn out.

There are just too many questions and there is too little time to just 'enjoy' the forum.  I am not actually trying to answer any questions but I do want everyone else to get credit for what they do.  I know some of you are looking at other's answers and some are giving thumbs up which is great.  Maybe you could actually put a short post saying that you have checked it and it is alright - then I won't feel like I have to check and I won't feel guilty about giving a tick when I have not personally checked.  This is just a thought.

Does anyone have any other ideas.

I have not responded to a number of messages.  I appologise for this. It is partly because the message system is still not very good and partly because I am just to busy with the immediate needs of the forum.

Enjoy the rest of your Friday.

Melody.

It is just 6 Rs out of 100 total = 6/100

this is not a difficult question.

Where is Rom and Bertie when you need them?

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

The following:  

$$\lim h\rightarrow0\frac{3x+h}{x+h}$$ (in Texmaker go to Math/Math functions to get \lim)gives:

$$$$\lim h\rightarrow0\frac{3x+h}{x+h}$$$$

but I don't know how to get the h->0 to go just beneath lim. We need a LaTeX expert!

That is really cool,

Thanks Bertie. 

SO now I am a bit confused.

Does (-1)^(4/3) have lots of answers ?

1 and $$\frac{-1-i\sqrt3}{2}$$  are just 2 of them?

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?

The notation is sloppy isn't it ?

Is it (-1)^4 divided by 3, (and why should the 4 come first, that only happens because the fraction is written on a single line, why not (-1)^(1/3) raised to the power 4 ?), or is it (-1)^(4/3) ?

Enclosing the 4/3 in brackets easily removes the ambiguity, and as this hasn't been done,  my interpretion would be the same as Melody's.

Speaking of Melody, was it yesterday that she asked about

$$e^{i\pi}=-1$$   ?

In which case,

$$(-1)^{4/3}=(e^{i\pi})^{4/3}=e^{4i\pi/3}$$

$$=\cos(4\pi/3)+i\sin(4\pi/3)$$

$$=-\frac{1}{2}-i\frac{\sqrt{3}}{2}.$$

There will of course be two other complex 'answers' one of which is the real number 1.

First you put the words into math

girls 

x+15

boys

x  

adults

a=x/10

a=5

so first you figure out the amount of boys

swith a=x/10 plug in 5 5=x/10 and switch the ten to the other side so 5*10=x

= 50=x

so x=50

x+15 is

50+15 

whih equals 65

there are 65 girls 

The left-hand side is an upward curving quadratic and the right-hand side is a straight line with a positive slope that cuts through the quadratic at two points.  To see this draw curves of y = x²+x-12 and y = 4x on the same graph

Treat it as an equality first and find the two values of x that solve the equality, then the values of x in between those two give the range in which the inequality holds.

There is a Chi-square test function in Excel:  

CHISQ.TEST(actual_range,expected_range)

Search CHISQ in Excel's help file.

Energy of photons is proportional to frequency, so inversely proportional to wavelength.  Therefore the ratio of ultraviolet to average energy is (1/3*10^-7)/(1/5.6*10^-7) = 5.6/3 (because the 10^-7s cancel).  So ultraviolet energy is 

$${\frac{{\mathtt{5.6}}}{{\mathtt{3}}}} = {\mathtt{1.866\: \!666\: \!666\: \!666\: \!666\: \!7}}$$times greater than the average.

Let the common length be x. Then the perimeter is 2x + (2x-2) or 4x-2, so we must have 4x-2 = 1.8

$${\mathtt{x}} = {\frac{\left({\mathtt{1.8}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}{{\mathtt{4}}}} = {\mathtt{x}} = {\mathtt{0.95}}$$metres

 The third side is then 2*0.95 - 2 which is less than zero!  So there is a problem with the question specification!

With log to the base 10 this is saying log₁₀x = 0.3142, what is x?

From definition of logarithm this means x = 10^0.3142 so:

$${\mathtt{x}} = {{\mathtt{10}}}^{{\mathtt{0.314\: \!2}}} = {\mathtt{x}} = {\mathtt{2.061\: \!579\: \!086\: \!952\: \!637\: \!4}}$$

This is 2.0616 to four decimal places.

This requires conservation of energy.  Kinetic energy at the bottom of the hill equals the sum of kinetic and potential energies at the top.

KE at bottom = (1/2)mv₁², where m is mass and v₁ is velocity at bottom (35.9ms^-1)

PE at top = mgh, where g is gravitational acceleration (9.81ms^-2) and h is height if hill (17.9m)

KE at top = (1/2)mv₂²,  so

(1/2)mv₂² + mgh = (1/2)mv₁² 

The mass cancels throughout, so

(1/2)v₂² +9.81*17.9 = (1/2)35.9²,

Multiply throughout by 2

v₂² + 2*9.81*17.9 = 35.9²,  

See if you can take it from here!

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!