VCE Methods Question Thread!

[pi]

Usually "b to the power of four"

[martin1106]

 For this question, I am asked to find the median.
 instead of solving the integral (let m= median)
 
 Why I cannot solve it in this way  ?

 Thanks

[b^3]

Remember you would need to integrate the area under the and not just take it away.

Although the first method is easier in this case.

[martin1106]

Remember you would need to integrate the area under the and not just take it away.

Although the first method is easier in this case.

Eh...forgot to integrate "1/8", thank you

[Homer]

1)  The function with rule f(x) = 3tan(x) + sin (x/2) has period____?

2) If a>0, b>0 and f : [0,b] --> R, f(x) = square-root[(x(2a-x))], then f will have an inverse function provided "b" is ____?

[soccerboi]

Probably a simple and stupid question but i dont know the answer to it.

Why does 0! =1?
If for example 3! means 3 X 2 X 1, then doesnt that mean 0! is 0?

Thanks

[TrueTears]

just a definition lol

[soccerboi]

How would you sketch this without calculator?

[TrueTears]

should have a similar shape to a cubic of that form

[soccerboi]

oh ok, so when the power is an odd number, the graph will just have a simply shape to a cubic? And if its an even power, it will look similar to a quartic?

[BubbleWrapMan]

Pretty much

[Hutchoo]

oh ok, so when the power is an odd number, the graph will just have a simply shape to a cubic? And if its an even power, it will look similar to a quartic?

Yes, that's right. Just be careful with the reciprocals though.
i.e 1/x^2 looks completely different from 1/(x^2+1)

[rife168]

Probably a simple and stupid question but i dont know the answer to it.

Why does 0! =1?
If for example 3! means 3 X 2 X 1, then doesnt that mean 0! is 0?

Thanks

Also realise that nCr for n=r will equal 1 because essentially 'there can only be one combination of n objects selected from n objects'

so nCr =

but if n=r then we get

nCn =

Which simplifies to   and we know that this must equal 1 so then it follows that 0!=1

That isn't necessarily exhaustive or general, but I appreciated this reasoning more than 'just a definition' haha.

[redxman]

Can anyone help me with the 2010 Exam 2 Paper: Question 20 MC

Question 20

[Lasercookie]

From x = zero to x = a, f(x) cuts or is above the x-axis.





From there, we can rule out all but D and E.

You can think about what transformation has been applied to the function to figure this out. This is probably the easiest method, probably because you don't really need to do too much working out, it's mostly intuitive and you can reason it out in your head.

So --> the function f(x) has been dilated by a factor of 5 parallel to the x-axis. So f(x) has been 'stretched', by a factor of 5. The average value of the function wouldn't change, all we've done is stretch it out sideways.

What is the average value of f(a)? I don't think I need to explain how to find the average value, but basically the average value is the height of the rectangle with the same area of a given segment of the function.

, the Area is a and the length is a --> so W (the average value) is 1.

Now what if that function has been stretched out by 5? What happens to the area?


So 

I'll include this method for the sake of including it. You don't have to worry about this if you don't know how to do it, but figured it might be useful for some. If you wanted a more algebraic way, you could use spesh maths knowledge and use integration by substitution.