Melody

What does this question mean please Geno?

24.1294560865187199

nearest hundreth means 2 decimal places

Look at the first 3 decimal places - the rest is of no conseqence     24.129

The nine is a big number (5,6,7,8,9 are all big numbers)

So the 2 in the second place goes up to 3

the answer is 24.13

Try looking at this thread and see if you can work it out

y=-3x-4

The y interecept is -4.   This is just a point  (0,-4)  So mark this on the y axis.

now

The gradient is        $$-3\; =\; \frac{-3}{1}$$

Now if a line has a negative gradient this means that the top of it will be on the LEFT hand side of the page.

Starting at the y intercept.   Go up 3 spaces.  Then go side ways 3 spaces in the LEFT (or neg) direction.

Mark the point where you end up.  

Join the points and you have your line.   

You should write the equation of the line on the line  

I think that you want an equal sign in your first equation.

Do you want these solved simultaneously?

-5x+y=-2         (1a)   change this to     y=5x-2    (1b)   (I added 5x to both sides)

-3x+6y=-12      (2a)

Now substitute 1b into 2a

-3x+6(5x-2)=-12

simplify and when you get a valuse for x sub it back inot one of the original equations to get a value for y.

Will  you be right to do it now?    

c)

$$\\\displaystyle\lim_{x\rightarrow \infty}\;\;\frac{sin(x^2)+10}{x^2+10}\\\\
Now\\
-1\le sin(x^2)\le 1\\
9\le sin(x^2)+10\le 11\\
$Therefore the numerator is a positive number between 9 and 11$\\
$Therefore$\\
\\\displaystyle\lim_{x\rightarrow \infty}\;\;\frac{sin(x^2)+10}{x^2+10}=0$$

Thank you Chris,

I haven't finished with this question yet but I have put it in the Sticky Thread "Great answers to Learn from"  :)

Yes Geno you may be right.  I was thinking about this as well.  My initial thought was that it was undefined but then I hunted about on the net and found people disagreed with me.

There seemed to be a concesous of opinion that 0^0 was defined as 1  ( this is just one site that said this - there were others)

I repeat!

I just worked out a.   you have to multiply top and bottom by the conjugate of the top and then it just falls out. 

It is quite simple this way.  :)

$$\displaystyle\lim_{x\rightarrow 0} \frac{\sqrt{2x+4}-2}{x}\\\\
=\displaystyle\lim_{x\rightarrow 0} \frac{\sqrt{2x+4}-2}{x}\times \frac{\sqrt{2x+4}+2}{\sqrt{2x+4}+2}\\\\
=\displaystyle\lim_{x\rightarrow 0} \frac{(2x+4)-4}{x(\sqrt{2x+4}+2)}\\\\
=\displaystyle\lim_{x\rightarrow 0} \frac{2}{(\sqrt{2x+4}+2)}\\\\
=\frac{2}{(\sqrt{2*0+4}+2)}\\\\
=\frac{2}{4}\\\\
=\frac{1}{2}$$

$$\\\frac{5^7}{5^7}=5^{7-7}=5^0\\\\
$but$\\\\
$any non-zero number divided by itself $\\\\
so\\\\
5^0=1\\\\
$Anything (including 0) raised to the 0 power is 1 $$$