VCE Methods Question Thread!

[Lasercookie]

Got stuck with this:

integrate sin^2(x) using integration by parts

can someone please help ?!

This isn't a methods question. You don't need to use integration by parts for this anyway, just use regular spesh methods?

Just use the identity
--> rearrange for sin^2(x)

[Jenny_2108]

h'(x) = (n/x-1)x^ne^{-x}

stationary point when x = n.

h''(n) < 0 since n is a positive integer

so local max

hey TT, can we use h''(x) to determine its local max/min/point of inflexion?
I thought it was in spesh only and the examiners don't allow us to apply spesh knowledge which isn't in methods
In methods they determine via stating the nature of turning point?!?

[pi]

You can use second derivatives as proof in methods afaik

[paulsterio]

I wouldn't though, to be honest, it's much faster to just substitute a point to the left and to the right of the stationary point into the first derivative.

Look at it this way, it's either you make two substitutions or one differentiation and one substitution, whichever is easier for you I guess.

[FlorianK]

h'(x) = (n/x-1)x^ne^{-x}

stationary point when x = n.

h''(n) < 0 since n is a positive integer

so local max

hey TT, can we use h''(x) to determine its local max/min/point of inflexion?
I thought it was in spesh only and the examiners don't allow us to apply spesh knowledge which isn't in methods
In methods they determine via stating the nature of turning point?!?

Explain?

[TrueTears]

h'(x) = (n/x-1)x^ne^{-x}

stationary point when x = n.

h''(n) < 0 since n is a positive integer

so local max

hey TT, can we use h''(x) to determine its local max/min/point of inflexion?
I thought it was in spesh only and the examiners don't allow us to apply spesh knowledge which isn't in methods
In methods they determine via stating the nature of turning point?!?

Explain?

h''(x) = 0 -> point of inflection

[FlorianK]

h'(x) = (n/x-1)x^ne^{-x}

stationary point when x = n.

h''(n) < 0 since n is a positive integer

so local max

hey TT, can we use h''(x) to determine its local max/min/point of inflexion?
I thought it was in spesh only and the examiners don't allow us to apply spesh knowledge which isn't in methods
In methods they determine via stating the nature of turning point?!?

Explain?

h''(x) = 0 -> point of inflection

x^4 ?

[TrueTears]

h(x) =/= x^4

[brightsky]

yeah technically speaking if h''(x) = 0, the stationary point can be anything..local max, local min or stationary point of inflection. i'd refrain from using techniques that aren't listed on the methods study design though.

[Hutchoo]

Can someone please explain how to do b)?

The answer for a) is a = 2/15.

Thank you

[Lasercookie]

The median is when the probability is equal to 0.5

So let's check the triangle bit first (x = 0 to x = 5):
.

That's not quite 1/2. We need 1/6th more area to find the median. What cut of the rectangle will get us to this value?



So the median occurs at

To double check that is actually the median, to should also have an area of 0.5


edit: fixed typo

[b^3]

The median will be reached when the area under the probability density function is 0.5. Since there are two sections that have areas under them, we need to check whether the median lies in the first area first, and g from there.

So the area under the first section is

so that means our median is in the second part.
So basically what  we are doing is
Let m=the median

Then solve for m (just replace the integrals with the areas, as it makes it simpler).


I've probably over complicated it a bit when explaning through it though.

EDIT: beaten by laseredd

[Hutchoo]

Thanks guys, you're top blokes.

[dinosaur93]

which paper is this question from?

[Hutchoo]

neap 2011. q5